Basic Maths Grand Test - Q4

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For what values of the constant c is the function f continuous on (-\infty ,\infty ) ?

$$f(x) = \begin{cases} cx^2+2x , &\text{ if }x < 2 ;\\ 2x+4 , &\text{ if } x \geq 2. \end{cases}$$

 

A. 0

B. 1

C. 2

D. 3

asked Nov 17 in Basic Maths by gbmentor (85,520 points)
reshown Nov 20 by getgatebook

1 Answer

0 votes

Given that function f is continuous on (-\infty ,\infty )

It means f is continuous on x=2  also.

So \lim_{x\rightarrow 2-}f(x) =\lim_{x\rightarrow 2+}f(x)=f(x)

4c+4=4+4

c=1

So option B is correct.

answered Nov 20 by tspranaykumar562 (2,720 points)
Answer:
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