Question

- If f(x) = 3x² − 4 and g(x) = 2x − 6, what is g(f(2))?

Answer 1

Answer:

$g[f(2)] = 10$

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=3x^2-4\\g(x)=2x-6\end{cases}$

Find f(2) by substituting $x = 2$ into function f(x):

$\begin{aligned}\implies f(2)& =3(2)^2-4\\& = 3(4)-4\\& = 12-4\\& = 8\end{aligned}$

Now substitute the found value of f(2) into function g(x):

$\begin{aligned}g[f(2)] & = 2[f(2)]-6\\\implies g[f(2)] & =2(8)-6\\& = 16-6\\& = 10\end{aligned}$

Answer 2

$\\ \rm\Rrightarrow g(f(2))$

$\\ \rm\Rrightarrow g(3(2)²-4)$

$\\ \rm\Rrightarrow g(12-4)$

$\\ \rm\Rrightarrow g(8)$

$\\ \rm\Rrightarrow 2(8)-6$

$\\ \rm\Rrightarrow 16-6$

$\\ \rm\Rrightarrow 10$