determine whether f and g are inverse functions by evaluation (fog)(x) and (gof)(x)

Question

f(x)=( 7/2)x-4 and (2x+8)/7 

Answer 1

Two functions are inverses if the composition of the functions equals x.  In other words, f and g are inverse functions if fog(x)=gof(x)=x.

f(g(x))=(7/2)(2x+8)/7-4=x+4-4=x

g(f(x))=(2((7/2)x-4)+8)/7=(7x-8+8)/7=x

So, f and g are inverses.