Question

If f(x)=x⁵ x³ x find f⁻1(3) and f(f⁻1(2)).

A. Inverse Function Calculation
B. Find Inverse of f(x)
C. f⁻1(3) and f(f⁻1(2)) Solver
D. Compute Inverse and Composition

Answer 1

To find the inverse of the function f(x) = x⁵ x³ x, set y = x⁵ x³ x and rearrange the equation. Then, substitute the given values into the equation to find the corresponding values of x and y.

Step-by-step explanation:

To find the inverse of the function f(x) = x⁵ x³ x, we need to solve for x in terms of y. We start by setting y = x⁵ x³ x and then rearrange the equation to isolate x. In this case, we can rewrite the equation as y = x⁸ x. To find f⁻¹(3), we substitute y = 3 into the equation and solve for x. Similarly, to find f(f⁻¹(2)), we first find f⁻¹(2) and then substitute the result into f(x).

To find f⁻¹(3), we have the equation 3 = x⁸ x. Let's solve this equation: 3 = x⁸ x => x⁸ x - 3 = 0. We can use numerical or graphical methods to find the value of x that makes the equation true. Once we find the value of x, we can substitute it back into the equation f(x) to find the corresponding value of y.

To find f(f⁻¹(2)), we first find f⁻¹(2) by solving the equation f(x) = 2. Once we find the value of x that makes this equation true, we substitute it back into the equation f(x) to find the corresponding value of y.