Find the inverse of the function. f(x) = 2x^3 - 4

Question

Please explain your steps :))

Answer 1

y = 2x³ - 4

x = 2y³ - 4

x - 4 = 2y³

(x - 4)/2) = y³

y = ³√((x - 4)/2) or ((x - 4)/2)^1/3

f^-1(x) = ³√((x - 4)/2) or ((x - 4)/2)^1/3

Answer 2

f(x) = 2x^3 - 4 (Given)

y = 2x^3 - 4 (Notational convenience)

x = 2y^3 - 4 (Just exchange x and y to make it the inverse function)

2y^3 = x + 4 (Switching left and right sides, and adding 4 to both sides)

y^3 = (x + 4) / 2

y = ³√((x + 4)/2), or [(x + 4)/2]^1/3 (Take the cubed root of both sides)

f^-1(x) = [(x + 4)/2]^1/3 (Give our result the proper inverse-function notation)

Use the desmos graphing calculator to verify that the function and the inverse are mirror images, with respect to the line y=x ... (why?)