Question

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

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

Answer 1

Answer: (A)

Given, $a \le f(x) \le b, f$ is strictly decreasing
$\therefore f^{-1}(a) \ge f^{-1} f(x) \ge f^{-1} (b)$
$\Rightarrow f^{-1} (b) \le x \le f^{-1} (a)$
$\Rightarrow x \in [f^{-1} (b) , f^{-1}(a)]$