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Composition of functions:determine the equation of (gof)(x) image attached much appreciated

Composition Of Functionsdetermine The Equation Of Gofx Image Attached Much Appreciated class=

Sagot :

In general, the definition of the function composition is given by the expression below

[tex](g\circ f)(x)=g(f(x))[/tex]

Therefore, in our case,

[tex](g\circ f)(x)=g(-\frac{1}{\sqrt{x}})=1(-\frac{1}{\sqrt{x}})^3+19(-\frac{1}{\sqrt{x}})^2+16=-\frac{1}{x^{\frac{3}{2}}}+\frac{19}{x}+16[/tex]

Then, the answer is

[tex]\Rightarrow(g\circ f)(x)=-\frac{1}{x^{\frac{3}{2}}}+\frac{19}{x}+16[/tex]

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