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Given f(x) = 3x + 6, find
f(f-l(f(x))).

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Final answer:

The expression f(f^{-1}(f(x))) simplifies to f(x) because applying the inverse function f^{-1} to f(x) results in the original input x, and then applying f to x gives f(x) again.

Therefore, f(f^{-1}(f(x))) equals 3x + 6.

Step-by-step explanation:

To solve for f(f^{-1}(f(x))), we need to understand the properties of the function f and its inverse f^{-1}.

The function f is given as f(x) = 3x + 6.

The inverse function f^{-1}(x) is the function that, when applied to f(x), returns the original input x.

Since applying f^{-1} to f(x) should give us x, when we apply f to that result, we should once again obtain f(x).

Specifically, f(f^{-1}(f(x))) simplifies to f(x).

Therefore, no matter what input x we choose, as long as f(x) is defined and f and its inverse f^{-1} are proper inverses, the result will always be f(x), which in this case is 3x + 6.

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