A function is defined by g(x)= (5-2x) x+1

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A function

g

is defined by

g(x)=\frac{\ln(5-2x)}{\sqrt{x+1}}, \quad x \neq -1.

Assume

\ln

denotes the natural logarithm. (a) Determine the set of all real numbers

x

for which

g(x)

is defined. (b) Explain why

g

is continuous on every open interval contained in its domain. (c) Express

g

’s interval(s) of continuity using interval notation.