Question

given f(-1)=2 find f^-1(2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find f^(-1)(2), we need to find the input value that gives an output of 2 when plugged into the function f(x).

Since f(-1) = 2, this means that when x = -1, the output (or f(x)) is equal to 2.

So f^(-1)(2) = -1.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the inverse function, f^(-1)(x), given that f(-1) = 2, you can follow these steps:

Step 1: Start with the equation f(x) = y, since we are looking for the inverse function.

Step 2: Replace y with x in the equation: x = f(y).

Step 3: Switch the variables x and y: y = f^(-1)(x).

Step 4: Now, we need to find the value of f^(-1)(x) when x = 2. So, we substitute x = 2 in the equation: y = f^(-1)(2).

Step 5: Since f(-1) = 2, it means f(x) = 2 when x = -1. So, we have f(-1) = 2 = y.

Step 6: Substitute y = 2 in the equation y = f^(-1)(x), we get 2 = f^(-1)(2).

Therefore, the value of f^(-1)(2) is 2.

Answer 3

[AI-generated answer — Explain Bot]

To find f^(-1)(2), we want to determine the input value that maps to an output of 2 under the inverse function of f.

First, let's understand what it means for f^(-1)(2) to be equal to -1.

The notation f^(-1)(2) means "the inverse of the function f applied to the input value of 2." In other words, we are looking for the input value of f that gives us an output of 2 when we apply f^(-1).

Since we are given f(-1) = 2, it means that f maps the input value -1 to the output value 2. In other words, f(-1) = 2.

To find the inverse function f^(-1), we need to swap the input and output values of f. So, if f(-1) = 2, the inverse function f^(-1) will have f^(-1)(2) = -1.

Therefore, f^(-1)(2) is equal to -1.