I need help on these two questions since I don't quite understand. Someone explain the steps on figuring them out.

"Find [fog][x] and [gof][x]
1. f(x)=2x-3
g(x)=x^2-2x

2. f(x)=x^2-9
g(x)=x+4

Question

I need help on these two questions since I don't quite understand. Someone explain the steps on figuring them out.

"Find [fog][x] and [gof][x]
1. f(x)=2x-3
    g(x)=x^2-2x

2. f(x)=x^2-9
    g(x)=x+4

anonymous · Answer

first get rid of the circle, and write 
$$f\circ g(x)=f(g(x))$$
then work from the inside out

anonymous · Answer

$$f(g(x))$$ replace the general $g(x)$ by the specific one you have, and write 
$$f(g(x))=f(x^2-2x)$$

anonymous · Answer

now comes the only tricky part
$$f(x)=2x-3$$ is like $f(\diamondsuit)=2\diamondsuit -3$
replace $\diamondsuit$ by $x^2-2x$ using parentheses and get 
$$f(x^2-2x)=2(x^2-2x)-3$$

anonymous · Answer

then some algebra to clean it up
$$2(x^2-2x)-3$$ distribute the $2$ to get 
$$2x^2-4x-3$$

anonymous · Answer

final answer is 
$$f\circ g(x)=2x^2-4x-3$$

anonymous · Answer

$$g\circ f(x)$$ method is the same, algebra is a bit more 
$$g\circ f(x)=g(f(x))=g(2x-3)=(2x-3)^2-2(2x-3)$$

anonymous · Answer

Thank you so much!

anonymous · Answer

yw
hope you can now do the second one by mimicking the first two examples
always works the same way