Question

Let $f$ be a strictly decreasing function with range $[a,b]$ then domain of the function $f$ is

• A. $\left[f^{-1}\right(b),f^{-1}(a\left)\right]$
• B. $[b,a]$
• C. $\left[f^{-1}\right(a),f^{-1}(b\left)\right]$
• D. none of these

Answer 1

The correct option is A $\left[f^{-1}\right(b),f^{-1}(a\left)\right]$

Given, $a\le f\left(x\right)\le b,$

$f$ is strictly decreasing $\therefore f^{-1}\left(a\right)\ge f^{-1}f\left(x\right)\ge f^{-1}\left(b\right)$

$\Rightarrow f^{-1}\left(b\right)\le x\le f^{-1}\left(a\right)$

Hence domain of $f$ is,$x\in [f^{-1}\left(b\right),f^{-1}\left(a\right)]$