let f x x 2 x 3 x 4 and g x 788020267

Let $$f\left( x \right) = \left| {x - 2} \right| + \left| {x - 3} \right| + \left| {x - 4} \right|$$ and $$g\left( x \right) = f\left( {x + 1} \right).$$ Then :

A. $$g\left( x \right)$$ is an even function

B. $$g\left( x \right)$$ is an odd function

C. $$g\left( x \right)$$ is neither even nor odd

D. $$g\left( x \right)$$ is periodic

Answer : $$g\left( x \right)$$ is neither even nor odd

Solution :
Function mcq solution image

$$\eqalign{ & g\left( x \right) = f\left( {x + 1} \right) = \left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \cr & {\text{If }}x < 1,\,\,\,g\left( x \right) = - x + 1 - x + 2 - x + 3 = - 3x + 6 \cr & {\text{If 1}} \leqslant x < 2,\,\,\,g\left( x \right) = x - 1 - x + 2 - x + 3 = - x + 4 \cr & {\text{If 2}} \leqslant x < 3,\,\,\,g\left( x \right) = x - 1 + x - 2 - x + 3 = x \cr & {\text{If }}x \geqslant 3,\,\,\,g\left( x \right) = x - 1 + x - 2 + x - 3 = 3x - 6 \cr} $$

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

Let $$f\left( x \right) = \left| {x - 2} \right| + \left| {x - 3} \right| + \left| {x - 4} \right|$$ and $$g\left( x \right) = f\left( {x + 1} \right).$$ Then :

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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Let $$f\left( x \right) = \left| {x - 2} \right| + \left| {x - 3} \right| + \left| {x - 4} \right|$$ and $$g\left( x \right) = f\left( {x + 1} \right).$$ Then :

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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Calculus >> Function

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