JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q72

MathematicsSingle correct+4 / -1Question 72 of 90

Let $f$ and $g$ be two differentiable functions on $\mathbb R$ such that $f'(x)>0$ and $g'(x)<0$ , for all $x\in\mathbb R$ . Then for all $x$ :

f(g(x))>f(g(x-1))

f(g(x))>f(g(x+1))

g(f(x))>g(f(x-1))

g(f(x))<g(f(x+1))

Answer and worked solution

Official answer: B

$f$ is increasing and $g$ decreasing, so $f\circ g$ is decreasing. Hence $f(g(x))>f(g(x+1))$ .

JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 72