(f o f^-1)(-10)

Please help solve this composition of an inverse function.

let's see now ...

Isn't by definition
(f o f^-1)(x) = x ?

so (f o f^-1)(-10) =-10

f(x)=10x-10

To solve the composition (f o f^-1)(-10), we need to find the value of f^-1(-10) first, and then substitute that value into the function f.

1. Let's assume that f(x) = y.
2. Since f^-1 is the inverse function of f, f^-1(f(x)) = x.
3. Let's substitute x = -10 into f^-1(f(x)):
f^-1(f(-10)) = -10.
4. This means that f^-1(-10) = -10.

Now, we have to substitute the value of f^-1(-10) into f.

5. Let's assume f(x) = 2x + 3.
6. Substitute x = -10:
f(-10) = 2(-10) + 3 = -20 + 3 = -17.

Therefore, (f o f^-1)(-10) = -17.

To solve the composition of an inverse function, we need to understand what an inverse function is. An inverse function is a function that reverses the effect of another function. In other words, if you take a value, apply a function to it, and then apply the inverse function to the result, you will get back the original value.

Given the function f and its inverse f^(-1), we want to find the value of (f o f^(-1))(-10).

To solve this, follow these steps:

Step 1: Apply the inverse function f^(-1) to the input value of -10.
- This means we need to find the value that, when plugged into f^(-1), will give us -10 as the output.
- Without the specific functions, it's impossible to provide an exact solution. However, I will guide you through the general process.

Step 2: Apply the function f to the result from Step 1.
- Once you have obtained a value from Step 1, plug it into f and evaluate.

By following these steps, you can find the value of (f o f^(-1))(-10).