Question

If a function f(x) is defined on [1,4] $\to$ [1,7] and given that f(3) = 5 and its inverse exists then find $f\left(f^{-1}\right(5\left)\right)$.

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Answer 1

We are given that f(3) = 5, according to the definition of inverse we can say $f^{-1}\left(5\right)$ = 3.

We have to find $f\left(f^{-1}\right(5\left)\right)$

$f\left(f^{-1}\right(5\left)\right)$ = f (3) [ as $f^{-1}\left(5\right)$ = 3 ]

f(3) = 5 [given]

so, f $\left(f^{-1}\right(5\left)\right)$ = 5 .