anyone good at composite functions ?

Question

anonymous · Answer

What's your question?

joftheworld · Answer

attachment

anonymous · Answer

$$f(x)=3x-9\
g(x)=x^2$$
So
$$(g\circ f)(x)=g(f(x))=g(3x-9)=(3x-9)^2$$

joftheworld · Answer

can you explain that step by step ?

anonymous · Answer

A composite function is a function of a function. What this means is that you replace the independent variable of the outermost function with the innermost function:
$$g(x)~~\Rightarrow~~g(f(x))$$
So wherever you see an $x$ in the expression for $g(x)$, you would replace it with $f(x)$.
For example, if $f(x)=x+2$, and $g(x)=3\color{red}x$, then
$$g(\color{red}{f(x)})=g(\color{red}{x+2})=3\color{red}{(x+2)}$$

joftheworld · Answer

so is g(x+2) = 3(x+2) the answer?

anonymous · Answer

No. Everything in my last post is an example. Refer to the comment above that.

joftheworld · Answer

so whats the answer?

anonymous · Answer

$$(g\circ f)(x)=(3x-9)^2~~\Rightarrow~~(g\circ f)(5)=(3(5)-9)^2$$
Compute the rest. I've done more than enough.

joftheworld · Answer

so (15-9)(15-9) ?