Question
Asked Sep 12, 2019
9 views

Find the value of the constant cc that makes the following function continuous on (−∞,∞)(−∞,∞).

 

f(x)={cx+7 if x∈(−∞,7], cx^2−7 if x∈(7,∞)

 

I tried to format this as best I could, but it is supposed to be a piecewise function. 

check_circle

Expert Answer

Step 1

We have been given a piecewise function and we need to determine the value of ‘c’ at which the given function is continuous on all real numbers.

cx7
f(x)= 7
x <= 7
x> 7
help_outline

Image Transcriptionclose

cx7 f(x)= 7 x <= 7 x> 7

fullscreen
Step 2

Since both the pieces of the given piecewise function are polynomials, therefore, we only need to check continuity at the point where the two pieces split, that is, x=7.

...
cx+ 7
f(x)= 7
x <= 7
x > 7
RHL = f(7)
LHL
c(7)+7= c(7)-7
7c 7 49c-7
42c 14
14
42
1
3
help_outline

Image Transcriptionclose

cx+ 7 f(x)= 7 x <= 7 x > 7 RHL = f(7) LHL c(7)+7= c(7)-7 7c 7 49c-7 42c 14 14 42 1 3

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Continuity

Related Calculus Q&A

Find answers to questions asked by student like you

Show more Q&A add