Knowee
Questions
Features
Study Tools

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) = x^3 + 2 is ____________

a. f^{-1} = (y – 2)^{1/2}
b. f^{-1} = (y – 2)^{1/3}
c. f^{-1} = 1/3
d. f^{-1} = (y – 2)

🧐 Not the exact question you are looking for?Go ask a question

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:

  1. Set y = x^3 + 2
  2. Subtract 2 from both sides to isolate the cubic term: y - 2 = x^3
  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).

This problem has been solved

Similar Questions

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)

f(x) = x – 2. Find the inverse of f(x).A.𝑓−1(𝑥)=𝑥−2f −1 (x)=x−2B.𝑓−1(𝑥)=2𝑥f −1 (x)=2xC.𝑓−1(𝑥)=𝑥+2f −1 (x)=x+2D.𝑓−1(𝑥)=2−𝑥f −1 (x)=2−x

Which of the following is the inverse of F(x) = -2x + 3?A.B.C.D.SUBMITarrow_backPREVIOUS

.(3,-19)is point of y = 2f(x - 1)+2      then point of y = 2 f(¹/₃x - 1)+2 is*(-3,14)(-9,-14)(3,14)(9,-14)

If f(x) = 3𝑥−3x−33​ , then f -1(x) =A.3𝑥+3x+33​ B.𝑥−333x−3​ C.3(𝑥+1𝑥)3( xx+1​ )D.No inverse exists.E.𝑥+3𝑥xx+3​

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.