Question

Ignore c. I only need help with a and b

Answer 1

Part A.

The composition of f ang g is given by

`(f\circ g)(x))=f(g(x))=((3x+7)-7)/(3)`

where we have inserted 3x-7 in the place of x in function f. Then, we have

`(f\circ g)(x))=f(g(x))=(3x+7-7)/(3)=(3x)/(3)=x`

Therefore, the answer is

`(f\circ g)(x))=x`

Part B

Similarly to the previous case, we have

`(g\circ f)(x))=g(f(x))=3((x+7)/(3))-7`

which gives

`(g\circ f)(x))=g(f(x))=x+7-7=x`

then, the answer is

`(g\circ f)(x))=x`

Part C.

In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.

Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).