Let f: [ 2,5 ] [ 2,5 ] be a bijective function such that d dx ( f… - Vidyadip

MCQ

Let $f:\left[ {2,5} \right] \to \left[ {2,5} \right]$ be a bijective function such that $\frac{d}{{dx}}\left( {{f^{ - 1}}\left( x \right)} \right) > 0\ \forall x \in \left[ {2,5} \right]$, then $\int\limits_2^5 {\left( {f\left( x \right) + {f^{ - 1}}\left( x \right)} \right)} dx$ is

A
$0$
B
$4$
C
$25$
✓
$21$

✓

Answer

Correct option: D.

$21$

d
$ \int_{a}^{b}\left(f(x)+f^{-1}(x) d x\right.=b f(b)-a f(a) $

$=5(5)-2(2)=25-4=21 $

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