Question

given F(x)=3x+5 and G(x)=x^2
a. (f o g)(x)
b.(g o f) (x)
c.(f o g) (-x)

Answer 1

First step is to make sure of their domain and range.
D(F)=R, R(F)=R
D(G)=R, R(G)=R/R-
So, all three are possible. as R(F) is subset to D(G) and vice versa.
I'll do the first one as example.
\[ (f o g)(x)=f(g(x))=f(x^2)=3x^2 + 5\]
i.e just substitute g(x) into x.
The others are similar.

Answer 2

@Shadowys so how do you do (c)?

Answer 3

I'll substitute -x for x but since g(x) is an even function,
g(-x)=g(x) and (f o g)(x)=(f o g) (-x)

Answer 4

@Shadowys basically a and c are the same?

Answer 5

Yes. note this is a special case of g(x).

Answer 6

@Shadowys Thankkkss

Answer 7

:)