Question

Ignore c. I only need help with a and b

Answer 1

Part A.

The composition of f ang g is given by

$(f\circ g)(x))=f(g(x))=\frac{(3x+7)-7}{3}$

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

$(f\circ g)(x))=f(g(x))=\frac{3x+7-7}{3}=\frac{3x}{3}=x$

Therefore, the answer is

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

Part B

Similarly to the previous case, we have

$(g\circ f)(x))=g(f(x))=3(\frac{x+7}{3})-7$

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).