Find the inverse of the function y2 squareroot in x 5 algebr

Find the inverse of the function y=2 squareroot in x -5 algebraically. Write down a polynomial function with real coefficients that has the given zeroes: -2, 2i and -2i.

Solution

y = (lnx -5)^1/3    (this is what i can see from the image)

So, to find inverse : plug x= y and y = x , then solve for y:

x = (lny - 5)^1/3

x^3 = lny - 5

lny = 5+ x^3

y = e^(x^3+5)

f^-1(x) = e^(x^3+5)

2) Polynomila iwth coefficients x = -2 , 2i , -2i

So, f(x) = (x+2)(x- 2i)(x+2i)

= (x+2)(x^2 + 4)

= x^3 +4x + 2x^2 +8

= x^3 + 2x^2 + 4x + 8