Operações e composição com funções

Nessa seção, exploraremos as possibilidades de operações e composição com funções
Operações com funções
Considere as f(x) e g(x). É possível realizar operações com essas funções:[br][br][table][tr][td][b]Operação [/b][/td][td][b]Entrada[/b][/td][/tr][tr][td][math]h\left(x\right)=f\left(x\right)+g\left(x\right)[/math][/td][td]h(x)=f(x)+g(x)[/td][/tr][tr][td][math]\text{h(x)=f(x) \cdot g(x)[br]}[/math][/td][td]h(x)=f(x)*(x)[br][/td][/tr][tr][td][math]h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}[/math][/td][td]h(x)=f(x)/g(x)[/td][/tr][tr][td][math]h\left(x\right)=f\left(x\right)^{g\left(x\right)}[/math][/td][td]h(x)=f(x)^g(x)[/td][/tr][/table]
Tente você mesmo
Sendo [math]f\left(x\right)=x^2[/math], [math]g\left(x\right)=x^3[/math] e [math]h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}[/math], construa a função h(x).
Visualização de sistema de 2 equações lineares de duas variáveis
Através do GeoGebra, é possível obter a solução de equações lineares. Observe a solução do seguinte sistema linear:[br][img]data:image/png;base64,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[/img][br]
Para construir a solução de um sistema linear no GeoGebra:[br][list][*]Construa as equações [/*][*]Crie as interseções entre os gráficos. (A interseção pode ser realizada através da ferramenta [icon]/images/ggb/toolbar/mode_intersect.png[/icon] Interseção de Dois Objetos ou com o comando Interseção( <Objeto>, <Objeto> )[/*][/list]
Tente você mesmo
Resolva a equação linear abaixo utilizando construções no GeoGebra:[br][img]data:image/png;base64,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[/img]
Outros materiais
Materiais que podem contribuir com seu aprendizado: [br][url=https://www.geogebra.org/m/XUv5mXTm#material/jj47ydyb]Tutorial GeoGebra Teams: "System of linear equations" (Sistema de equações lineares)[br][/url][url=https://ogeogebra.com.br/site/textos/8.pdf]OGeoGebra - Texto "Funções"[/url]

Bilgi: Operações e composição com funções