Use the value you found for Latex: f(x)

Question

f
(
x
)
to find Latex: f^{-1}\left(f(x)\right)\textsf{.} For example, if Latex: f(x)=3\textsf{,} find Latex: f^{-1}(3)\textsf{.} List the order of operations that you used to find the value.

Answer 1

To find the value of Latex: f^{-1}\left(f(x)\right), we need to substitute the value of Latex: f(x) into the inverse function Latex: f^{-1}. The order of operations is as follows:

1. Start with the function Latex: f(x).
2. Substitute the value of Latex: f(x) into the inverse function.
3. Simplify the expression to find Latex: f^{-1}\left(f(x)\right).

For example, if Latex: f(x)=3, to find Latex: f^{-1}(3):

1. Start with the function Latex: f(x)=3.
2. Substitute the value of Latex: f(x)=3 into the inverse function: Latex: f^{-1}(3).
3. Simplify the expression to find the value of Latex: f^{-1}(3).

Note: The specific form of the inverse function Latex: f^{-1} will depend on the original function Latex: f(x).