Find k so that the following function is constant on any interval f(x)=(x^2+k if x<=5);(kx if x>5)

klupko5HR

klupko5HR

Answered question

2022-11-25

Find k so that the following function is constant on any interval
f ( x ) = { x 2 + k if  x 5 k x   if  x > 5

Answer & Explanation

Omari Lane

Omari Lane

Beginner2022-11-26Added 10 answers

A function f is continuous on an interval if
lim x a f ( x ) = f ( a )
for every value a in the interval. It is also known that polynomials are continuous everywhere. Your function
f ( x ) = { x 2 + k if  x 5 k x if  5 < x
will therefore be continuous if lim x 5 f ( x ) = f ( 5 ). To accomplish this goal, we can evaluate both polynomials in the piecewise definition of f at 5 and set them equal:
5 2 + k = 5 k .
Solving for k we obtain k = 25 4 and so
f ( x ) = { x 2 + 25 4 if  x 5 25 4 x if  5 < x .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?