Question

Given f(x)=3x^6, find f^-1(x) then state whether f^-1(x) is a function

Answer 1

Option c.

Explanation:

Given,

f(x) = y = 3x^6

To find f^-1(x), we just need to replace y with x, and x with y

x = 3*y^6

Now we solve for y

f(x)^-1 = y = ±(x/3)^(1/6)

To quickly see if it is a function, we can plot it using an graphing calculator or any plotting tool.

Please see attached picture.

By looking at the plot, we can tell f(x)^-1 is not a function, because for a single value of x, there are two corresponding values of y

Correct answer:

Option C.