Question:medium
Let $f(x) = \begin{cases} \cos x & \text{if } x \geq 0 \\ -\cos x & \text{if } x<0 \end{cases}$. Which one of the following statements is not true?
Let $f(x) = \begin{cases} \cos x & \text{if } x \geq 0 \\ -\cos x & \text{if } x<0 \end{cases}$. Which one of the following statements is not true?
Show Hint
When looking for discontinuities in piecewise functions, focus your attention on the points where the function definition changes. If the limits from both sides don't "meet," the function is not continuous there.
Updated On: May 2, 2026
- $f(x)$ is continuous at $x = 1$
- $f(x)$ is continuous at $x = -1$
- $f(x)$ is continuous at $x = 2$
- $f(x)$ is continuous at $x = -2$
- $f(x)$ is continuous at $x = 0$
Show Solution
The Correct Option is
Solution and Explanation
Was this answer helpful?
0
Top Questions on Continuity
- The function \(f(x) = x - |x - x^2|\), \(-1 \le x \le 1\) is continuous on
- BITSAT - 2017
- Mathematics
- Continuity
- Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]: I. f(x) is continuous in [-1,1]. II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?
- BITSAT - 2016
- Mathematics
- Continuity
- Let \[ f(x)= \begin{cases} \dfrac{1-\sin^3 x}{3\cos^2 x}, & x < \dfrac{\pi}{2} \\ [6pt] p, & x = \dfrac{\pi}{2} \\ [6pt] \dfrac{q(1-\sin x)}{(\pi-2x)^2}, & x > \dfrac{\pi}{2} \end{cases} \] If \(f(x)\) is continuous at \(x=\dfrac{\pi}{2}\), then \((p,q)=\)
- BITSAT - 2014
- Mathematics
- Continuity
- If the function \( f(x) = ax + b \), \( 2 < x < 4 \), is continuous at \( x = 2 \) and 4, then the values of \( a \) and \( b \) are:
- BITSAT - 2012
- Mathematics
- Continuity
- Want to practice more? Try solving extra ecology questions todayView All Questions
