Question

If a function \[ f:[1,7]\rightarrow\mathbb{R} \] is defined as \[ f(x)= \begin{cases} 2x^2-1, & x\le\sqrt7,[2mm] \sqrt{7x}+6, & \sqrt7[2mm] \sin\pi x, & 5\le x\le6,[2mm] x-[x], & 6<x\le7, \end{cases} \] then the number of points of discontinuity in \([1,7]\) is

• A. \(4\)
• B. \(3\)
• C. \(2\)
• D. \(1\)

Hint:

For piecewise functions, check continuity only at the junction points by comparing the left-hand limit, right-hand limit, and the function value.

Answer 1

The Correct Option is D