Question 369117
(Note: Please put multiple term numerators and denominators in parentheses. As you posted it, {{{g(x) = x -9/4}}} which is NOT the inverse of f(x). What you meant was {{{g(x) = (x-9)/4}}} which should be posted as g(x) = (x-9)/4. Tutors are more likely to help when the problems are posted clearly.<br>
To determine if functions f and g are inverses of each other, find f(g(x)) and g(f(x)). They should be equal to x.<br>
{{{f(g(x)) = f((x-9)/4) = 4((x-9)/4) + 9 = cross(4)((x-9)/cross(4)) + 9 = (x-9) + 9 = x}}}<br>
{{{g(f(x)) = g(4x+9) = ((4x+9) - 9)/4 = (4x)/4 = (cross(4)*x)/cross(4) = x}}}<br>
f(g(x)) = g(f(x)) = x. So f anf g are inverses of each other.