Find the inverse

Question

Find the inverse of f(x) = 3√(x) + 5

The inverse is ? , where x ≥ 5

Answer 1

y = 3 * sqrt(x) + 5

x = 3 * sqrt(y) + 5 <--- swaps x and y

x-5 = 3 * sqrt(y)

(x-5)^2 = 9 y

(x-5)^2/9 = y

-------------------------

check:

f(f_inv(x)) = 3 * sqrt(( x-5)^2/9 )+5

= 3 * (x-5)/3 + 5

= x-5 + 5

= x

and

f_inv(f(x)) = ( (3 * sqrt(x) + 5) - 5) ^ 2 / 9

= ( ( 3 * sqrt(x))^2/9

= 9 * x/ 9

= x