JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\) and \(g\) be two functions defined by \(f(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\|x-1|, & x \geq 0\end{array} \text { and } g(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\1, & x \geq 0\end{array}\right. \text {. }\right.\) Then (gof) (x) is
- A Differentiable everywhere
- B Continuous everywhere but not differentiable exactly at one point
- C Not continuous at \(x =-1\)
- D Continuous everywhere but not differentiable at \(x=1\)
Answer & Solution
Correct Answer
(B) Continuous everywhere but not differentiable exactly at one point
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{c}x+1, \quad x < 0 \\ 1-x, \quad 0 \leq x<1 \\ x-1,1 \leq x\end{array}\right.\) \(g(x)=\left\{\begin{array}{c} x +1, x < 0 \\ 1, x \geq 0\end{array}\right.\) \(g(f(x))=\left\{\begin{array}{c} x +2, x < -1 \\ 1, x \geq-1\end{array}\right.\)…
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