# Basic Maths Grand Test - Q4

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

reshown Nov 20

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 (2,720 points)