f(x)=x^2-5 and g(x)=6x, then g(f(x)) is equal to
i know the answer is 6x^2-30 but i don't know how.

Question

watermelon14 · Answer

@ikram002p ?

hero · Answer

Well, let's see:
$\begin{align*}g(f(x)) &= 6(f(x)) \&=6(x^2 - 5) \&=6x^2 - 30\end{align*} $

watermelon14 · Answer

oh but for g why is it not 6x

hero · Answer

You were given:
$g(x) = 6x$

In the next step, you replace $x$ with $f(x)$ to get this:

$g(f(x)) = 6(f(x))$

hero · Answer

And so that particular step is called "substitution".

jhonyy9 · Answer

@watermelon14 you dont understand it ?

watermelon14 · Answer

no i understand it but it is a bit confusing still why the x goes away

jhonyy9 · Answer

where and what x goes ?

hero · Answer

Because they asked you to find $g(f(x))$. If you notice, when you substitute $x$ with $g(x)$ the result is $g(f(x))$. And only at that point are you able to find the appropriate expression.

hero · Answer

If they asked you to find $g(6)$ how would you find it? You would have to replace the $x$ with $6$.

watermelon14 · Answer

ohh yes now i see. thanks!