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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