Question

If f(x) = x - 3, g(x) = 3x - 9, and h(x) = x^2-6x+9, then (gf)(2)=

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given functions

$\begin{gathered} f(x)=x-3 \\ g(x)=3x-9 \\ h(x)=x^2-6x+9 \end{gathered}$

STEP 2: Find the gf(2)

$\begin{gathered} \left(gf\right)\left(x\right)=g\left(x\right)f\left(x\right) \\ =g\left(2\right)f\left(2\right) \end{gathered}$

Find g(2)

$\begin{gathered} x=2 \\ By\text{ substitution,} \\ g(2)=3(2)-9=6-9=-3 \end{gathered}$

Find f(2)

$\begin{gathered} x=2 \\ By\text{ subsitution,} \\ f(2)=2-3=-1 \end{gathered}$

Find gf(2)

$\begin{gathered} By\text{ multiplication,} \\ =-3\cdot-1=3 \end{gathered}$

Hence, the answer is 3