Consider the functions and on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the functions

f(x)=\sqrt{x+1}

and

g(x)=x

on the interval

[0,1]

. Determine whether the graphs of

f

and

g

are guaranteed to intersect on this interval, and justify your conclusion using values of

f(x)-g(x)

at the endpoints.