Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(1).f(x) = 3x^2 – 5x – 1 g(x) = 2x – 12

Answer 1

Remember that, for the definition of a function composition:

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

Then:

$(f\circ g)(1)=f(g(1))$

Evaluate g taking x=1 :

$\begin{gathered} g(x)=2x-12 \\ \Rightarrow g(1)=2(1)-12 \\ =2-12 \\ =-10 \end{gathered}$

Since g(1)=-10, then:

$f(g(1))=f(-10)$

Evaluate f at x=-10:

$undefined$