Question

if $f(x) = x^2 + 7x$ and $g(x) = 3x - 1$, what is $f(g(x))$?
$\bigcirc$ $9x^2 + x + 1$
$\bigcirc$ $9x^2 + 15x - 6$
$\bigcirc$ $9x^2 + 21x - 6$
$\bigcirc$ $9x^2 - 27x$

Explanation:

Step1: Substitute $g(x)$ into $f(x)$

$f(g(x))=(3x-1)^2 + 7(3x-1)$

Step2: Expand the squared term

$(3x-1)^2 = 9x^2 - 6x + 1$

Step3: Expand the linear term

$7(3x-1)=21x - 7$

Step4: Combine all terms

$9x^2 - 6x + 1 + 21x - 7 = 9x^2 + 15x - 6$

Answer:

$\boldsymbol{9x^2 + 15x - 6}$ (Option: $9x^2 + 15x - 6$)