Question

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

• A. 3
• B. 5
• C. 1
• D. 7

Answer 1

The correct option is B 5

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 .