Prove that the functions f(x)=x+2, if x=<1 and f(x)=x^2. if x>1 are discontinuous. 

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The function f(x) is defined such that f(x) = x + 2 , if x <= 1 and f(x) = x^2, if x > 1.

At the point x = 1, if we approach from the left

lim x--> 1- [ f(x)] = 1 + 2 = 3.

If we approach from the right,

lim x--> 1+ [f(x)] = 1^2 = 1

The value of lim x--> 1- [ f(x)] is not equal to lim x--> 1+ [f(x)].

Therefore the function is discontinuous.

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial