Question

Let f(x) = 2x - 6 . Solve f⁻¹(x) when x = 2 .

a) -5
b) 4
c) -2
d) 0

Answer 1

To solve f⁻¹(x) when x = 2 for the given function f(x) = 2x - 6, we swap the x and y variables, solve for y, and substitute x = 2 into the inverse function. The value of f⁻¹(x) when x = 2 is 4.

Step-by-step explanation:

To solve f⁻¹(x) when x = 2, we need to find the value of the inverse function of f(x) = 2x - 6.

1. Start with the given function: f(x) = 2x - 6.
2. Replace f(x) with y: y = 2x - 6.
3. Swap the x and y variables: x = 2y - 6.
4. Solve for y: y = (x + 6) / 2.
5. Now we have the inverse function: f⁻¹(x) = (x + 6) / 2.
6. Substitute x = 2 into the inverse function: f⁻¹(2) = (2 + 6) / 2 = 8 / 2 = 4.

Therefore, the value of f⁻¹(x) when x = 2 is 4.