The inverse of function f(x) = x3 + 2 is ____________a.f -1 = (y – 2) 1/2b.f -1 = (y – 2) 1/3c.f -1 = 1/3d.f -1 = (y – 2)
Question
The inverse of function f(x) = x3 + 2 is ____________a.f -1 = (y – 2) 1/2b.f -1 = (y – 2) 1/3c.f -1 = 1/3d.f -1 = (y – 2)
Solution
The inverse of a function is found by switching the x and y values. This means we set y = x^3 + 2 and solve for x. Here are the steps:
- Set y = x^3 + 2
- Subtract 2 from both sides to isolate the cubic term: y - 2 = x^3
- Take the cube root of both sides to solve for x: x = (y - 2)^(1/3)
So, the inverse of the function f(x) = x^3 + 2 is f^-1(y) = (y - 2)^(1/3). Therefore, the correct answer is b. f^-1 = (y – 2)^(1/3).
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