Question

The function f(x) is shown below

x: -6,-3,2,5,8
f(x): 1,2,5,3,0
If g(x) is the inverse of f(x), what is the value of f(g(2))?

Answer 1

To solve for f(g(2)), we determine that g(2) equals -3 because f(-3) = 2. Then, f(g(2)) equates to f(-3), which equals 2.

Step-by-step explanation:

To find the value of f(g(2)) when g(x) is the inverse of f(x), we must first understand what an inverse function is. The inverse function g(x) essentially reverses the operation of f(x).

In the given function f(x), we find the x-value that corresponds to an f(x) value of 2. Looking at the provided function values, we see that f(-3) = 2. Therefore, g(2) must equal -3, since g(x) and f(x) are inverses.

Now, we substitute -3 into the function f(x) to get f(g(2)) = f(-3). Since we know that f(-3) = 2, the value of f(g(2)) is therefore 2.

To evaluate f(g(2)) when g(x) is the inverse of f(x), we first identify that g(x) reverses the operation of f(x). Given f(x) such that f(-3) = 2, we determine that g(2) = -3, as g(x) and f(x) are inverses. Substituting (-3) into f(x), we obtain f(g(2)) = f(-3), and since f(-3) = 2, the value of f(g(2)) is 2.