Solveeit Logo
Login

Question

Question: If fog = \|sin x\| and gof = sin<sup>2</sup>\(\sqrt{x}\) then f(x) and g(x) are:...

If fog = |sin x| and gof = sin2x\sqrt{x} then f(x) and g(x) are:

A

f(x) =sin⁡ 6mux\sqrt{\sin\mspace{6mu} x}, g(x) = x2

B

f(x) = |x|, g(x) = sin x

C

f(x) =x\sqrt{x}, g(x) = sin2x

D

f(x) = sinx\sqrt{x}, g(x) = x2

Answer

f(x) =x\sqrt{x}, g(x) = sin2x

Explanation

Solution

fog = f(g(x)) = |sin x| = sin⁡2x\sqrt{\sin^{2}x}.

Also gof = g(f(x)) = sin2x\sqrt{x}.

Obviously, sin⁡2x\sqrt{\sin^{2}x} = g(x)\sqrt{g(x)} and sin2x\sqrt{x} = sin2(f(x))

i.e. g(x) = sin2x and f(x) = x\sqrt{x}