Find the inverse of the function.

Question

Find the inverse of the function.

 

1.  f(x) = 1/16 x⁴, x≥0

 

2.  f(x) = 2x+5/3

 

Please help me out on these problems I would really appreciate it. Thank you so much for your time.

Answer 1

To find the inverse of a function we need to change x to y (that is f(x)) and to solve for y. 

1. f(x) =y = 1/16x⁴, x≥0. Inverse: x = 1/16 y⁴, y≥ 0. Or y⁴ = x/(1/16) = 16x, y = 4th root of 16x , or y = 2*(4th root of x).  In other words: f(x) = 2 √x, where you must write by hand little # 4 ot the top of radical sign. 

 

2. Inverse for y= f(x) = 2x + 5/3, We'll flip y and x now: x= 2y + 5/3, then 2y = x - 5/3, or y = (1/2) x  - 5/6 = f(x)

Answer: f(x) = (1/2)x -5/6