The domain of f( x ) = sin ^ - 1( 1 + x^22x ) + sqrt 1 - x^2 is :

the domain of f x sin 1 1 x 22x 1 x 2 is 472020206

The domain of $$f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{1 + {x^2}}}{{2x}}} \right) + \sqrt {1 - {x^2}} \,$$ is :

A. $$\left\{ 1 \right\}$$

B. $$\left( { - 1,\,1} \right)$$

C. $$\left\{ {1,\, - 1} \right\}$$

D. none of these

Answer : $$\left\{ {1,\, - 1} \right\}$$

Solution :
Here $$\left| {\frac{{1 + {x^2}}}{{2x}}} \right| \leqslant 1$$ and $$1 - {x^2} \geqslant 0.$$ The first inequality implies $$x=1,\,-1,$$ which satisfy the second inequation.

Releted MCQ Question on
Calculus >> Function

Releted Question 1

Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is:

A. Injective but not surjective

B. Surjective but not injective

C. Bijective

D. None of these.

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Releted Question 2

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$ is strictly above the $$x$$-axis if and only if

A. $$k < 7$$

B. $$ - 5 < k < 7$$

C. $$k > - 5$$

D. None of these.

View Answer

Releted Question 3

Let $$f\left( x \right) = \left| {x - 1} \right|.$$ Then

A. $$f\left( {{x^2}} \right) = {\left( {f\left( x \right)} \right)^2}$$

B. $$f\left( {x + y} \right) = f\left( x \right) + f\left( y \right)$$

C. $$f\left( {\left| x \right|} \right) = \left| {f\left( x \right)} \right|$$

D. None of these

View Answer

Releted Question 4

If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$ then

A. $$0 \leqslant x \leqslant 4$$

B. $$x \leqslant - 2\,{\text{or}}\,x \geqslant 4$$

C. $$x \leqslant 0\,{\text{or}}\,x \geqslant 4$$

D. None of these

View Answer

The domain of $$f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{1 + {x^2}}}{{2x}}} \right) + \sqrt {1 - {x^2}} \,$$ is :

Releted MCQ Question on
Calculus >> Function

Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is:

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$ is strictly above the $$x$$-axis if and only if

Let $$f\left( x \right) = \left| {x - 1} \right|.$$ Then

If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$ then

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The domain of $$f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{1 + {x^2}}}{{2x}}} \right) + \sqrt {1 - {x^2}} \,$$ is :

Releted MCQ Question on Calculus >> Function

Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is:

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$ is strictly above the $$x$$-axis if and only if

Let $$f\left( x \right) = \left| {x - 1} \right|.$$ Then

If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$ then

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