Define f(x)= ( 2x+1 x-4 )

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Define

f(x)=\ln\left(\frac{2x+1}{x-4}\right), \qquad x\in\mathbb R.

(i) Determine the domain of

f

. (ii) List all real numbers where

f

fails to be continuous. (iii) Write the interval(s) on which

f

is continuous. (iv) For each discontinuity obtained in part (ii), state its nature (removable, jump, or infinite) with justification.