Question

Let f(x) = x + 2 and g(x) = x2 + 4. Find f(g(f(2)).

Answer 1

`f(g(f(2)))=22`

Explanation:

The given functions are

`f(x)=x+2`

and

`g(x)=x^2+4`

We want to find
`f(g(f(2))`.

We first find
`f(2)=2+2=4`

This implies that we are finding
`f(g(4)`.

`f(g(x))=f(x^2+4)`

`\Rightarrow f(g(x))=x^2+4+2`

`\Rightarrow f(g(x))=x^2+6`

This implies that;

`\Rightarrow f(g(4))=4^2+6`

`\Rightarrow f(g(4))=16+6`

`\Rightarrow f(g(4))=22`

`\therefore f(g(f(2)))=22`