Question

F(x) = Square root of quantity x plus nine.; g(x) = 8x - 13

Find f(g(x)).

Answer 1

`\bf \begin{cases} f(x)=√(x+9)\\\\ g(x)=8x+13 \end{cases}\qquad (f\circ g)(x)\iff f(\ g(x)\ )=\sqrt{\boxed{g(x)}+9} \\\\\\ thus\qquad f(\ g(x)\ )=\sqrt{\boxed{8x+13}+9}`

simplify it away

Answer 2

The answer will be :
`2√(2x-1)`

Explanation:

f(x) = Square root of quantity x plus nine.

Mathematically we can write this as:

`f(x)=√(x+9)`

`g(x)=8x-13`

Now, we have to find
`f(g(x))`

So, we will replace x in f(x) with : 8x-13.

`f(g(x))=f(8x-13)`

=
`√(8x-13+9)`

=
`√(8x-4)`

=
`√(4(2x-1))`

=
`2√(2x-1)`

Hence, answer is : f(g(x)) =
`2√(2x-1)`