(A) Given $g(f(x)) = |\sin x| = \sqrt{\sin^2 x}$.Also,$f(g(x)) = \sin^2 \sqrt{x}$.Comparing $g(f(x)) = \sqrt{\sin^2 x}$ with $g(f(x))$,we can infer $f

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

$f(x) = \sin^2 x, g(x) = \sqrt{x}$

(A) Given $g(f(x)) = |\sin x| = \sqrt{\sin^2 x}$.Also,$f(g(x)) = \sin^2 \sqrt{x}$.Comparing $g(f(x)) = \sqrt{\sin^2 x}$ with $g(f(x))$,we can infer $f(x) = \sin^2 x$ and $g(x) = \sqrt{x}$.Let us verify this:If $f(x) = \sin^2 x$ and $g(x) = \sqrt{x}$,then $g(f(x)) = g(\sin^2 x) = \sqrt{\sin^2 x} = |\sin x|$.And $f(g(x)) = f(\sqrt{x}) = \sin^2(\sqrt{x}) = (\sin \sqrt{x})^2$.Both conditions are satisfied.Therefore,the correct option is $A$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

If $g(f(x)) = |\sin x|$ and $f(g(x)) = (\sin \sqrt{x})^2$,then

IIT 1998 All IIT

A
$f(x) = \sin^2 x, g(x) = \sqrt{x}$
B
$f(x) = \sin x, g(x) = |x|$
C
$f(x) = x^2, g(x) = \sin \sqrt{x}$
D
$f$ and $g$ cannot be found

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Chemistry Questions

Chapter

Data Entry - Chemistry

Subtopic

Level 0 of all question bank

Previous Year

IIT 1998 Paper All IIT years →

$A$ ping-pong ball of mass $m$ is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed $v$ and just after collision the water falls dead,the mass flow rate of water in the nozzle is equal to

View Solution

$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are respectively:

AP EAMCET 2007

View Solution

Which among the following reactions will take place spontaneously?

View Solution

For which of the following pairs of complexes is the crystal field splitting energy $\Delta_0$ for $II > \Delta_0$ for $I$?

$I$ $II$

$(a). [Cr(H_2O)_6]^{2+}$ $[Cr(H_2O)_6]^{3+}$

$(b). [Fe(H_2O)_6]^{3+}$ $[Fe(CN)_6]^{3-}$

$(c). [Fe(CN)_6]^{3-}$ $[Ru(CN)_6]^{3-}$

$(d). [NiF_6]^{4-}$ $[NiF_6]^{2-}$

$I$	$II$
$(a). [Cr(H_2O)_6]^{2+}$	$[Cr(H_2O)_6]^{3+}$
$(b). [Fe(H_2O)_6]^{3+}$	$[Fe(CN)_6]^{3-}$
$(c). [Fe(CN)_6]^{3-}$	$[Ru(CN)_6]^{3-}$
$(d). [NiF_6]^{4-}$	$[NiF_6]^{2-}$