If f(x) = ^2x and the composite function g(f(x)) = | |, then g(x)… - Vidyadip

MCQ

If $f(x) = \sin^2x$ and the composite function $\text{g(f(x))} = |\sin\text{x}|,$ then $g(x)$ is equal to$:$

A
$\sqrt{\text{x}-1}$
✓
$\sqrt{\text{x}}$
C
$\sqrt{\text{x}+1}$
D
$-\sqrt{\text{x}}$

✓

Answer

Correct option: B.

$\sqrt{\text{x}}$

Given that $\text{f(x)}=\sin^2\text{x}$ and the composite function $\text{g(f(x))}=|\sin\text{x}|$
We will do it using trial and error method.
If we take $\text{g(x)}=-\sqrt{\text{x}}$ and $\text{f(x)}=\sin^2\text{x}$
$\text{g(f(x))}=\text{g}(\sin^2\text{x})$
$=-\sin\text{x}$
Which contradicts to the $\text{g(f(x))}=|\sin\text{x}|$
Hence, we take $\text{g(x)}=\sqrt{\text{x}}$
$\text{g(f(x))}=\text{g}(\sin^2\text{x})$
$=\sqrt{\sin^2\text{x}}=|\sin\text{x}|$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Functions→Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{x}=2\text{ at},\text{y}=\text{at}^2,$ where a is a constant, then $\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ at}\ \text{x}=\frac{1}{2}$ is:

$\frac{1}{2}\text{a}$
1
2a
None of these

Which of the termis not used in a linear programming problem:

Slack inequation
Objective function
Concave region
Feasible Region

If $\int\limits_{0}^{\frac{\pi}{2}}\sin\text{x}\cos\text{xdx}$ is equal to:

$\frac{1}{2}$
$\frac{1}{4}$
$2$
$1$

The value of the integral $\int\limits^2_{-2}\big|1-\text{x}^2\big|\text{dx}$ is:

4
2
-2
0

Consider the non-empty set consisting of children in a family and a relation $R$ defined as $a R b$ if $a$ is brother of $b$. Then $R$ is

$\int\text{x}^{\sin\text{x}}\Big(\frac{\sin\text{x}}{\text{x}}+\cos\text{x}\cdot\log\text{x}\Big)\text{dx}$ is equal to:

$\text{x}^{\sin\text{x}}+\text{C}$
$\text{x}^{\sin\text{x}}\cos\text{x}+\text{C}$
$\frac{(\text{x}^{\sin\text{x}})^2}{2}+\text{C}$
None of these.

If A and B are two events, then $\text{P}(\overline{\text{A}}\cap\text{B})=$

$\text{P}(\overline{\text{A}})\text{ P}(\overline{\text{B}})$
$1-\text{P}(\text{A})-\text{P}(\text{B})$
$\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
$\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$

Ratio in which the xy-plane divided the join of (1, 2, 3) and (4, 2, 1) is:

3 : 1 internally
3 : 1 externally
2 : 1 internally
2 : 1 externally

If $y=(\tan x)^{\sin x}$, then $\frac{d y}{d x}$ is equal to

Choose the correct answer in Exercises:
$\int\frac{10\text{x}^9+10^{\text{x}}\log_\text{e}10}{\text{x}^{10}+10^{\text{x}}}\text{ equals}$

$10^\text{x}-\text{x}^{10}+\text{C}$
$10^\text{x}+\text{x}^{10}+\text{C}$
$(10^\text{x}-\text{x}^{10})^{-1}+\text{C}$
$\log(10^\text{x}+\text{x}^{10})+\text{C}$