An inverse function, of a function [math]f[/math], is a function such that [math]f^{-1}\left(f\left(x\right)\right)=x[/math] for all x in the domain of [math]f[/math]and [math]f\left(f^{-1}\left(y\right)\right)=y[/math] for all y in the target of [math]f[/math]. [br][br]Informally we can think of [math]f^{-1}\left(x\right)[/math] undoing the work that [math]f(x)[/math] has done. Therefore, when evaluating [math]f^{-1}\circ f[/math] or [math]f\circ f^{-1}[/math], the original value, x, will be obtained.[br][br]The graph below shows the functions [math]f\left(x\right)=e^x[/math], [math]g(x)=ln(x)[/math] and the points A and B. By adjusting the values of [i]a[/i], you can move the points A and B.
Calculate f(a), for [math]a=2;a=0.5;a=-1[/math]
What values do you expect to obtain when calculating g(7.39), g(1.65) and g(0.37)?
[code][/code]Using the graph of [math]h\left(x\right)=x^3[/math] below, and your knowledge of inverse functions, can you estimate the values of [math]\sqrt[3]{2.2},\sqrt[3]{-6.86},\sqrt[3]{1.52}[/math]? What about [math]\sqrt[3]{x^3}[/math]?