Question

If f(x)=3x-4 and g(x)=9x^2-16, find f o g and g o f

Answer 1

Given that f(x)=3x-4 and g(x)=9x^2-16.

The value of f o g can be obtained as follows:

`\begin{gathered} f\circ g=f(g(x)) \\ =f(9x^2-16) \\ =3(9x^2-16)-4 \\ =27x^2-48-4 \\ =27x^2-52 \end{gathered}`

The value of g o f can be obtained as follows:

`\begin{gathered} g\circ f=g(f(x)) \\ =9(3x-4)^2-16 \\ =9(9x^2-24x+16)-16 \\ =81x^2-216x+144-16 \\ =81x^2-216x+128 \end{gathered}`