Question

consider the function
$f\left(x\right)=\{\begin{array}{ccc}a+bx,x<1& & \\ 4,x=1& & \\ b-ax,x>1& & \end{array}$
If ${lim}_{x\to 1}f\left(x\right)=f\left(1\right)$, then the values of a and b are

• A. a = 3, b = 1
• B. a = 1, b = 3
• C. a = 0, b = 4
• D. a = 4, b = 0

Answer 1

The correct option is C

a = 0, b = 4

Given ${lim}_{x\to 1}f\left(x\right)=f\left(1\right)\Rightarrow {lim}_{x\to 1^{-}}f\left(x\right)=f\left(1\right)\&{lim}_{x\to 1^{+}}f\left(x\right)=f\left(1\right)\Rightarrow a+b=4andb-a=4\Rightarrow a=0,b=4$