Question

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

Answer 1

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

`(g\circ f)(x)=g(f(x))`

Therefore, in our case,

`(g\circ f)(x)=g(-(1)/(√(x)))=1(-(1)/(√(x)))^3+19(-(1)/(√(x)))^2+16=-\frac{1}{x^{(3)/(2)}}+(19)/(x)+16`

Then, the answer is

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