Question

For the function f(x)=(10x^1/)-2, find f⁻¹(x)

A) f⁻¹(x) = ((x+2)/10)⁵
B) f⁻¹(x) = ((x+2)/10)^(1/5)
C) f⁻¹(x) = ((x/10) + 2)⁵
D) f⁻¹(x) = ((x/10) + 2)^(1/5)

Answer 1

To find the inverse function of f(x) = (10x^{1/5}) - 2, switch x and y and solve for y, which yields f^{-1}(x) = ((x + 2)/10)^{1/5}. The correct option is B) f^{-1}(x) = ((x + 2)/10)^{1/5}.

Step-by-step explanation:

The function given is f(x) = (10x1/5) - 2.

To find the inverse function, denoted as f∑(x), we need to switch x and y and solve for y. Here are the steps:

1. Let y = (10x1/5) - 2.
2. Switch x and y to get x = (10y1/5) - 2.
3. Add 2 to both sides to isolate the term with y: x + 2 = 10y1/5.
4. Multiply both sides by 1/5 to solve for y: y1/5 = (x + 2)/10.
5. Raise both sides to the power of 5 to get y by itself: y = (((x + 2)/10)1/5)5.
6. Simplify to get f∑(x) = (x + 2)/10.