If f:[1,10] arrow[1,10] is a non-decreasing function and g:[1,10] arrow[1,10] is a non-increasing function. Let h(x)=f(g(x)) with h(1)=1, then h(2)

Question

If f:[1,10] arrow[1,10] is a non-decreasing function and g:[1,10] arrow[1,10] is a non-increasing function. Let h(x)=f(g(x)) with h(1)=1, then h(2) (A) lies in (1,2) (B) is more than 2 (C) is equal to 1 (D) is not defined

Tardigrade Admin · Accepted Answer

x > 1 ⇒ f(x) ≥ f(1) x > 1 ⇒ g(x) ≤ g(1) ⇒ f(g(x)) ≤ f(g(1)) ⇒ h(x) ≤ 1 .....(i) Range of h(x) is subset of [1,10] ⇒ h(x) ≥ 1.....(ii) By (i), (ii) we have h(x)=1 ⇒ h(2)=1

Q. If $f : [1, 10] \to [1, 10]$ is a non-decreasing function and $g : [1, 10] \to [1, 10]$ is a non-increasing function. Let $h (x) = f (g (x))$ with $h (1) = 1$ , then $h (2)$

lies in $(1, 2)$

is more than 2

is equal to 1

is not defined

$x > 1 \Rightarrow f (x) \geq f (1)$
$x > 1 \Rightarrow g (x) \leq g (1)$
$\Rightarrow f (g (x)) \leq f (g (1))$
$\Rightarrow h (x) \leq 1.....$ (i)
Range of $h (x)$ is subset of $[1, 10]$
$\Rightarrow h (x) \geq 1.....$ (ii)
By (i), (ii) we have $h (x) = 1 \Rightarrow h (2) = 1$

Q. If f:[1,10]→[1,10] is a non-decreasing function and g:[1,10]→[1,10] is a non-increasing function. Let h(x)=f(g(x)) with h(1)=1, then h(2)

lies in (1,2)