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

Question

Let f be a strictly decreasing function with range [a, b] then domain of the function f is (A) [f-1 (b), f-1 (a)] (B) [b, a] (C) [f-1 (a), f-1 (b)] (D) None of these

Tardigrade Admin · Accepted Answer

Given, a le f(x) le b, f is strictly decreasing ∴ f-1(a) ge f-1 f(x) ge f-1 (b) ⇒ f-1 (b) le x le f-1 (a) ⇒ x ∈ [f-1 (b) , f-1(a)]

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

$[f^{- 1} (b), f^{- 1} (a)]$

$[b, a]$

$[f^{- 1} (a), f^{- 1} (b)]$

None of these

Given, $a \leq f (x) \leq b, f$ is strictly decreasing
$∴ f^{- 1} (a) \geq f^{- 1} f (x) \geq f^{- 1} (b)$
$\Rightarrow f^{- 1} (b) \leq x \leq f^{- 1} (a)$
$\Rightarrow x \in [f^{- 1} (b), f^{- 1} (a)]$

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

[f−1(b),f−1(a)]

[b,a]

[f−1(a),f−1(b)]