eqalign and let f x 4x 1 cr and 4x 1 leqslant x leqslant 0

\[f\left( x \right) = \left\{ \begin{array}{l} 4,\,x < - 1\\ - 4x,\, - 1 \le x \le 0. \end{array} \right.\]
If $$f\left( x \right)$$ is an even function in $$R$$ then the definition of $$f\left( x \right)$$ in $$\left( {0,\, + \infty } \right)$$ is :

A. \[f\left( x \right) = \left\{ \begin{array}{l} 4x,\,0 < x \le 1\\ 4x,\,x > 1 \end{array} \right.\]

B. \[f\left( x \right) = \left\{ \begin{array}{l} 4x,\,0 < x \le 1\\ - 4,\,x > 1 \end{array} \right.\]

C. \[f\left( x \right) = \left\{ \begin{array}{l} 4,\,0 < x \le 1\\ 4x,\,x > 1 \end{array} \right.\]

D. none of these

Answer : \[f\left( x \right) = \left\{ \begin{array}{l} 4x,\,0 < x \le 1\\ 4x,\,x > 1 \end{array} \right.\]

Solution :
Function mcq solution image

An even function is symmetrical about the $$y$$-axis.
Clearly from the graph, the definition given in option (A) is correct.

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.

View Answer

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

\[f\left( x \right) = \left\{ \begin{array}{l} 4,\,x < - 1\\ - 4x,\, - 1 \le x \le 0. \end{array} \right.\]
If $$f\left( x \right)$$ is an even function in $$R$$ then the definition of $$f\left( x \right)$$ in $$\left( {0,\, + \infty } \right)$$ 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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Function

Practice More MCQ Question on Maths Section

\[f\left( x \right) = \left\{ \begin{array}{l} 4,\,x < - 1\\ - 4x,\, - 1 \le x \le 0. \end{array} \right.\] If $$f\left( x \right)$$ is an even function in $$R$$ then the definition of $$f\left( x \right)$$ in $$\left( {0,\, + \infty } \right)$$ 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

Practice More Releted MCQ Question on Function

Practice More MCQ Question on Maths Section

\[f\left( x \right) = \left\{ \begin{array}{l} 4,\,x < - 1\\ - 4x,\, - 1 \le x \le 0. \end{array} \right.\]
If $$f\left( x \right)$$ is an even function in $$R$$ then the definition of $$f\left( x \right)$$ in $$\left( {0,\, + \infty } \right)$$ is :

Releted MCQ Question on
Calculus >> Function

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Function