A function is defined as follows: f(x)=\ array cc - x x^2 , & x ≠ 0 0, & x=0 array . Which one of the following is correct in respect of the above function?

Correct answer: C. f(x) is discontinuous at x=0 f(x)=\ array l -x x^2 , x ≠ 0 0, x=0 array .=\ array l (-x)/(|x|), x ≠ 0 0, x=0. array .f(0+h)= -h h =-1 ; f(0-h)= h h =1 So, f(x) is discontinuous at x=0 .

NDA 2017

Exam: NDA
Year: 2017
Subject: Mathematics
Chapter: Continuity and Differentiability

NDA 2017 · Mathematics · Continuity and Differentiability

A function is defined as follows: f(x)=\ array cc - x x^2 , & x ≠ 0...

A function is defined as follows:

f(\mathrm{x})=\left\{

\begin{array}{cc} -\frac{\mathrm{x}}{\sqrt{\mathrm{x}^2}}, & \mathrm{x} \neq 0 \\ 0, & \mathrm{x}=0 \end{array}

\right.

Which one of the following is correct in respect of the above function?

Options

A $f(\mathrm{x})$ is continuous at $\mathrm{x}=0$ but not differentiable at $\mathrm{x}=0$
B $f(x)$ is continuous as well as differentiable at $\mathrm{x}=0$
C $f(\mathrm{x})$ is discontinuous at $\mathrm{x}=0$
DNone of the above

Correct answer

C. $f(\mathrm{x})$ is discontinuous at $\mathrm{x}=0$

Step-by-step solution

f(x)=\left\{

\begin{array}{l}\frac{-x}{\sqrt{x^2}}, x \neq 0 \\ 0, x=0\end{array}

\right.=\left\{

\begin{array}{l}\frac{-x}{|x|}, x \neq 0 \\ 0, x=0.\end{array}

\right.\mathrm{f}(0+\mathrm{h})=\frac{-\mathrm{h}}{\mathrm{ h}}=-1 ; \mathrm{f}(0-\mathrm{h})=\frac{\mathrm{h}}{\mathrm{ h}}=1

So,

\mathrm{f}(\mathrm{x})

is discontinuous at

\mathrm{x}=0

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

What is the derivative of (x)/(|x|) with respect to x , where x< 0 ? NDA 2026 Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026 Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f ^ ∘ g(x) , then which… NDA 2026 Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of… NDA 2026 If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is… NDA 2026 Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026 Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025 For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025 For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the… NDA 2025 For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025 Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025 Paragraph: Let f(x)=[x]^2- [x^2] . Question: Consider the following statements: A. f(x)… NDA 2024 Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2024 Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023 Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023 Let f(x)=\ array cc a x(x+1)+b, & x < 1 x-1 & 1 ≤ x ≤ 2 array . If the function f(x) is… NDA 2023 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQs JEE Mathematics PYQs All NDA PYQs