Question

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

Answer 1

`\\ \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`

Answer 2

`g[f(2)] = 10`

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}`