the inverse of f(x)=3(3x+4) in function notation

Question

find the inverse in function notation

Answer 1

To find the inverse function, swap x and y and then solve for y.

y = 3(3x+4)

x = 3(3y+4)

3y+4 = x/3

g(x) = f^-1(x) = y = (x/3-4)/3

As a check, f(x)°g(x) must = x.

f(g(x)) = 3(3(x/3-4)/3 +4 = 3(x/3-4+4) = 3x/3 = x √