[tex]\\ \rm\Rrightarrow g(f(2))[/tex]
[tex]\\ \rm\Rrightarrow g(3(2)²-4)[/tex]
[tex]\\ \rm\Rrightarrow g(12-4)[/tex]
[tex]\\ \rm\Rrightarrow g(8)[/tex]
[tex]\\ \rm\Rrightarrow 2(8)-6[/tex]
[tex]\\ \rm\Rrightarrow 16-6[/tex]
[tex]\\ \rm\Rrightarrow 10[/tex]
Answer:
[tex]g[f(2)] = 10[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x^2-4\\g(x)=2x-6\end{cases}[/tex]
Find f(2) by substituting [tex]x = 2[/tex] into function f(x):
[tex]\begin{aligned}\implies f(2)& =3(2)^2-4\\& = 3(4)-4\\& = 12-4\\& = 8\end{aligned}[/tex]
Now substitute the found value of f(2) into function g(x):
[tex]\begin{aligned}g[f(2)] & = 2[f(2)]-6\\\implies g[f(2)] & =2(8)-6\\& = 16-6\\& = 10\end{aligned}[/tex]
