1. (a) Define inverse of function, [math] f:R\to R [/math][br]Solution:[br]If [math] f:A\to B [/math] is one to one onto function then the new function defined from B ot A is called inverse function. It is denoted by [math] f^{-1} : B\to A [/math] .[br][br](b) What is the relation between composition of a function and its inverse.[br]Solution:[br]The relation between composition of a function and its inverse is an identity function. [math] \therefore fof^{-1} (x ) =f^{-1}of(x) = x [/math][br][br]2. Represent the following functions in mapping diagram and find their inverse.[br][br](a) [math] f = \{ (1,2),(2,3),(4,5) \} [/math][br]Solution:[br][img]data:image/png;base64,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[/img][br][math] \therefore f^{-1} = \{ (2,1), (3,2), (5,4) \} [/math] [br][br](b) [math] g = \{ (1,4),(2,5),(3,6) \} [/math][br]Solution:[br][img]data:image/png;base64,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[/img][br][math] g^{-1} = \{ (4,1), (5,2), (6,3) \} [/math] [br][br](c) [math] h = \{ (-2,4),(-3,9),(-6,36) \} [/math][br]Solution:[br][img]data:image/png;base64,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[/img][br][math] h^{-1} = \{ (4,-2), (9,-3), (36,-6) \} [/math] [br][br]3. If [math] f [/math] is the real - valued function, find [br](a) [math] f^{-1}(x) [/math] (b) [math] f^{-1}(6) [/math] (c) [math] f^{-1}\left( \frac{1}{4} \right) [/math] (d) [math] f^{-1}(-2) [/math] in each of the following:[br](i) [math] f(x) = 3x+1 [/math][br]Solution:[br] [math] \begin{align} (a) \ \ [br]\text{Let } & y = f(x) \\[br]\text{or, } & y = 3x+1 \\[br]\text{or, } & y - 1 = 3x \\[br]\text{or, } & \frac{y-1}{3} = x \\[br]\text{or, } & x = \frac{y-1}{3} \\[br]\text{or, } & f^{-1}(y) = \frac{y-1}{3} \\ [br] \therefore \ \ & f^{-1}(x) = \frac{x-1}{3} [br] \end{align} [/math] [br] [math] \begin{align} (b) \ \ [br]\text{Now } & f^{-1}(x) = \frac{x-1}{3} \\[br]\text{or, } & f^{-1}(6) = \frac{6-1}{3} \\[br] \therefore \ \ & f^{-1}(6) = \frac{5}{3} \\[br] \end{align} [/math] [br] [math] \begin{align} (c) \ \ [br]\text{Now } & f^{-1}(x) = \frac{x-1}{3} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{\frac{1}{4}-1}{3} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{\frac{1-4}{4}}{3} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{-3}{12} \\[br]\therefore \ \ & f^{-1}(\frac{1}{4}) = \frac{-1}{4} \\[br] \end{align} [/math] [br] [math] \begin{align} (d) \ \ [br]\text{Now } & f^{-1}(x) = \frac{x-1}{3} \\[br]\text{or, } & f^{-1}(-2) = \frac{-2-1}{3} \\[br]\text{or, } & f^{-1}(-2) = \frac{-3}{3} \\[br] \therefore \ \ & f^{-1}(-2) = - 1 \\[br] \end{align} [/math] [br][br](ii) [math] f(x) = 2x - 5 [/math][br]Solution:[br] [math] \begin{align} (a) \ \ [br]\text{Let } & y = f(x) \\[br]\text{or, } & y = 2x-5 \\[br]\text{ Interchanging} & \text{ the the role of x and y we get,} \\[br]\text{or, } & x=2y-5 \\[br]\text{or, } & x+5 = 2y \\[br]\text{or, } & \frac{x+5}{2} = y \\[br]\text{or, } & y = \frac{x+5}{2} \\ [br] \therefore \ \ & f^{-1}(x) = \frac{x+5}{2} [br] \end{align} [/math] [br] [math] \begin{align} (b) \ \ [br]\text{Now } & f^{-1}(x) = \frac{x+5}{2} \\[br]\text{or, } & f^{-1}(6) = \frac{6+5}{2} \\[br] \therefore \ \ & f^{-1}(6) = \frac{11}{2} \\[br] \end{align} [/math] [br] [math] \begin{align} (c) \ \ [br]\text{Now } & f^{-1}(x) = \frac{x+5}{2} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{\frac{1}{4}+5}{2} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{\frac{1+20}{4}}{2} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{21}{8} \\[br]\therefore \ \ & f^{-1}(\frac{1}{4}) = \frac{21}{8} \\[br] \end{align} [/math] [br] [math] \begin{align} (d) \ \ [br]\text{Now } & f^{-1}(x) = \frac{x+5}{2} \\[br]\text{or, } & f^{-1}(-2) = \frac{-2+5}{2} \\[br]\text{or, } & f^{-1}(-2) = \frac{3}{2} \\[br] \therefore \ \ & f^{-1}(-2) = \frac{3}{2} \\[br] \end{align} [/math] [br][br](iii) [math] f(x) = \frac{x+1}{2} [/math][br]Solution:[br] [math] \begin{align} (a) \ \ [br]\text{Let } & y = f(x) \\[br]\text{or, } & y = \frac{x+1}{2} \\[br]\text{or, } & 2y=x+1 \\[br]\text{or, } & 2y-1=x \\[br]\text{or, } & x = 2y - 1 \\[br]\text{or, } & f^{-1}(y) = 2y-1 \\[br] \therefore \ \ & f^{-1}(x) = 2x-1 \\[br] \end{align} [/math] [br] [math] \begin{align} (b) \ \ [br]\text{Now } & f^{-1}(x) = 2x-1 \\[br]\text{or, } & f^{-1}(6) = 2\times 6 - 1 \\[br]\text{or, } & f^{-1}(6) = 12 - 1 \\[br] \therefore \ \ & f^{-1}(6) = 11 \\[br] \end{align} [/math] [br] [math] \begin{align} (c) \ \ [br]\text{Now } & f^{-1}(x) = 2x - 1 \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = 2\times \frac{1}{4} - 1 \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{1}{2} - 1 \\[br]\text{or, } & f^{-1}(\frac{1}{4}) = \frac{1-2}{2} \\[br]\therefore \ \ & f^{-1}(\frac{1}{4}) = \frac{-1}{2} \\[br] \end{align} [/math] [br] [math] \begin{align} (d) \ \ [br]\text{Now } & f^{-1}(x) = 2x - 1 \\[br]\text{or, } & f^{-1}(-2) = 2(-2) - 1 \\[br]\text{or, } & f^{-1}(-2) = -4 - 1 \\[br] \therefore \ \ & f^{-1}(-2) = -5 \\[br] \end{align} [/math] [br](iv) [math] f = \left\{ \left(x,\frac{x-2}{x+2}\right), x\neq -2 \right\} [/math] [br]Solution:[br] [math] \begin{align} (a) \ \ [br]\text{Given, } & \\[br] f & = \left\{ \left(x,\frac{x-2}{x+2}\right), x\neq -2 \right\} \\[br]\text{or, } & f(x) = \frac{x-2}{x+2}, x \neq - 2 \\[br]\text{Now, } & \\[br]\text{Let } & y = f(x) \\[br]\text{or, } & y = \frac{x-2}{x+2} \\[br]\text{or, } & xy+2y =x-2 \\[br]\text{or, } & 2y + 2 = x - xy \\[br]\text{or, } & 2y + 2 = x(1-y) \\[br]\text{or, } & \frac{2y + 2}{1-y} = x \\[br]\text{or, } & x = \frac{2y + 2}{1-y} \\[br]\text{or, } & f^{-1}(y) = \frac{2y + 2}{1-y} \\[br] \therefore \ \ & f^{-1}(x) = \frac{2x + 2}{1-x} \\[br] \end{align} [/math] [br] [math] \begin{align} (b) \ \ [br]\text{Now } & f^{-1}(x) = \frac{2x + 2}{1-x} \\[br]\text{or, } & f^{-1}(6) = \frac{2\times 6 + 2}{1- 6 } \\[br]\text{or, } & f^{-1}(6) = \frac{12 + 2}{-5} \\[br]\text{or, } & f^{-1}(6) = \frac{14}{-5} \\[br] \therefore \ \ & f^{-1}(6) = - \frac{14}{ 5} \\[br] \end{align} [/math] [br] [math] \begin{align} (c) \ \ [br]\text{Now } & f^{-1}(x) = \frac{2x + 2}{1-x} \\[br]\text{or, } & f^{-1}(\dfrac{1}{4}) = \dfrac{2\times \dfrac{1}{4} + 2}{1-\dfrac{1}{4}} \\[br]\text{or, } & f^{-1}(\dfrac{1}{4}) = \dfrac{\dfrac{1}{2} + 2}{\dfrac{4-1}{4}} \\[br]\text{or, } & f^{-1}(\dfrac{1}{4}) = \dfrac{\dfrac{1+4}{2}}{\dfrac{4-1}{4}} \\[br]\text{or, } & f^{-1}(\dfrac{1}{4}) = \dfrac{\dfrac{5}{2}}{\dfrac{3}{4}} \\[br]\text{or, } & f^{-1}(\frac{1}{4}) =\frac{5}{2}\times \frac{4}{3} \\[br]\therefore \ \ & f^{-1}(\frac{1}{4}) = \frac{10}{3} \\[br] \end{align} [/math] [br] [math] \begin{align} (d) \ \ [br]\text{Now } & f^{-1}(x) = \frac{2x + 2}{1-x} \\[br]\text{or, } & f^{-1}(-2) = \frac{2(-2) + 2}{1-(-2)} \\[br]\text{or, } & f^{-1}(-2) = \frac{-4 + 2}{1+2} \\[br] \therefore \ \ & f^{-1}(-2) = \frac{-2}{3} \\[br] \end{align} [/math] [br][br]4. If [math] f(x) = x + 1, g(x) = 2x, [/math] find[br][br](a) [math] (fog^{-1})(x) [/math] (b) [math] (gof^{-1}) (x) [/math]. [math] f [/math] and [math] g [/math] are real-valued functions.[br][br]Solution:[br] [math] \begin{align} (a) \ \ [br]\text{Let } & y_1 = g(x) \\[br]\text{or, } & y_1 = 2x \\[br]\text{or, } & \frac{y_1}{2} = x \\[br]\text{or, } & x = \frac{y_1}{2} \\[br]\text{or, } & f^{-1}(y_1) = \frac{y_1}{2} \\[br] \therefore \ \ & f^{-1}(x) =\frac{x}{2} \\[br]\text{Now, } & \\[br](fog^{-1})(x) & = f(g^{-1}(x)) \\[br]\ & = f \left( \frac{x}{2} \right) \\[br]\ & = \frac{x}{2} + 1 \\[br]\ & = \frac{x+2}{2} \\[br]\therefore (fog^{-1})(x) & = \frac{x+2}{2} \\[br] \end{align} [/math] [br] [math] \begin{align} (b) \ \ [br]\text{Let } & y_2 = f(x) \\[br]\text{or, } & y_2 = x+1 \\[br]\text{or, } & y_2 - 1 = x \\[br]\text{or, } & x = y_2 - 1 \\[br]\text{or, } & f^{-1}(y_2) = y_2 - 1 \\[br] \therefore \ \ & f^{-1}(x) = x - 1 \\[br]\text{Now, } & \\[br](gof^{-1})(x) & = g(f^{-1}(x)) \\[br]\ & = g( x - 1 ) \\[br]\ & = 2(x-1) \\[br]\therefore (fog^{-1})(x) & = 2(x-1) \\[br] \end{align} [/math] [br][br]5. (a) If [math] f(x) = 3x - 7, g(x) = \frac{x+2}{5} [/math] and [math] (g^{-1}of)(x) = f(x), [/math] find the value of [math]x [/math], \ \ [math] f \text{ and } g [/math] are real-valued functions.[br][br]Solution:[br] [math] \begin{align} (a) \ \ [br]\text{Let } & y = \frac{x+2}{5} \\[br]\text{or, } & 5y = x + 2 \\[br]\text{or, } & 5y - 2 = x \\[br]\text{or, } & x = 5y - 2 \\[br]\text{or, } & f^{-1}(y ) = 5y - 2 \\[br] \therefore \ \ & f^{-1}(x) = 5x - 2 \\[br]\text{Now, } & \\[br]\ &(g^{-1}of)(x) = f(x), \\[br]\text{or, } & g^{-1} ( f(x) ) = 3x - 7 \\[br]\text{or, } & g^{-1} ( 3x - 7 ) = 3x - 7 \\[br]\text{or, } & 5(3x-7) - 2 = 3x - 7 \\[br]\text{or, } & 15x -35 - 2 = 3x - 7 \\[br]\text{or, } & 15x -35 - 2 = 3x - 7 \\[br]\text{or, } & 15x - 37 = 3x - 7 \\[br]\text{or, } & 15x - 3x = 37 - 7 \\[br]\text{or, } & 12 x = 30 \\[br]\text{or, } & x = \frac{30}{12} \\[br]\text{or, } & x = \frac{5}{2} \\[br] \end{align} [/math] [br][br]5. (b) [math] f [/math] is real-valued function defined as [math] f(x) = 3x+a [/math]. If [math] (fof)(6) = 10 [/math] then find the values of [math] a [/math] and [math] f^{-1}(4) [/math].[br][br]Solution:[br] [math] \begin{align} [br]\text{Given,} & \\[br]\ & f(x) = 3x + a \\[br]\text{Now,} & \\[br]\ & (fof)(6) = 10 \\[br]\text{or, } & f(f(6)) = 10 \\[br]\text{or, } & f( 3\times 6 + a ) = 10 \\[br]\text{or, } & f( 18 + a ) = 10 \\[br]\text{or, } & 3(18+a) + a = 10 \\[br]\text{or, } & 54+3a + a = 10 \\[br]\text{or, } & 4a = 10-54 \\[br]\text{or, } & 4a = -44 \\[br]\text{or, } & a = \frac{-44}{4} \\[br]\text{or, } & a = - 11 \\[br]\therefore \ & f(x) = 3x - 11 \\[br]\text{Now,} & \\[br]\text{Let } & y = f(x) \\[br]\text{or, } & y = 3x -11 \\[br]\text{or, } & y +11 = 3x \\[br]\text{or, } & \frac{y +11}{3} = x \\[br]\text{or, } & x = \frac{y+11}{3} \\[br]\text{or, } & f^{-1}(y) = \frac{y+11}{3} \\[br]\text{or, } & f^{-1}(x) = \frac{x+11}{3} \\[br]\text{or, } & f^{-1}(4) = \frac{4+11}{3} \\[br]\text{or, } & f^{-1}(4) = \frac{15}{3} \\[br]\therefore \ \ & f^{-1}(4) = 5 \\[br] \end{align} [/math] [br] [br]6. Write the formula of volume and surface area of sphere in terms of radius. Find the functional relation and write their inverse.[br]Solution:[br] [math] \begin{align} [br]\text{Let radius of sphere be } x \\[br]\text{Then, volume of sphere } = \frac{4}{3} \pi x^3 \\[br]\therefore \ f(x) = \frac{4}{3} \pi x^3 \\[br]\text{To find inverse }\\[br]\text{Let } y = f(x) \\[br]\text{or, } y = \frac{4}{3} \pi x^3 \\[br]\text{or, } 3y = 4 \pi x^3 \\[br]\text{or, } \frac{3y}{4 \pi } = x^3 \\[br]\text{or, } \sqrt[3]{\frac{3y}{4 \pi } } = x \\[br]\text{or, } x = \sqrt[3]{\frac{3y}{4 \pi } } \\[br]\text{or, } f^{-1}(y) = \sqrt[3]{\frac{3y}{4 \pi } } \\[br]\therefore \ \ f^{-1}(x) = \sqrt[3]{\frac{3x}{4 \pi } } \\[br] \end{align} [/math] [br] [math] \begin{align} [br]\text{Let radius of sphere be } x \\[br]\text{Then, surface area of sphere } = 4 \pi x^2 \\[br]\therefore \ f(x) = 4 \pi x^2 \\[br]\text{To find inverse }\\[br]\text{Let } y = f(x) \\[br]\text{or, } y = 4 \pi x^2 \\[br]\text{or, } \frac{y}{4 \pi } = x^2 \\[br]\text{or, } \pm \sqrt{\frac{y}{4 \pi } } = x \\[br]\text{or, } x = \pm \sqrt{\frac{y}{4 \pi } } \\[br]\text{or, } f^{-1}(y) = \pm \sqrt{\frac{y}{4 \pi } } \\[br]\therefore \ \ f^{-1}(x) = \pm \sqrt{\frac{x}{4 \pi } } [br] \end{align} [/math] [br]