Question

$\text{If the function}f:R\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}x-2,\text{if}x<-1\\ 2,\text{if}-1\le x\le 1\\ x+3,\text{if}x>1\end{array}$
Find the value of $f\left(0\right)$.

• A. -2
• B. 2
• C. 3
• D. can't be found

Answer 1

The correct option is B 2

$\text{Given,}f\left(x\right)=\{\begin{array}{c}x-2,\text{if}x<-1\\ 2,\text{if}-1\le x\le 1\\ x+3,\text{if}x>1\end{array}$

For a given value of x = a, find out the interval at which the point a is located, there after find f (a) using the particular value defined in that interval.

Here, 0 lies in the 2nd interval. So for x = 0, $f\left(x\right)=2$

$\therefore f\left(0\right)=2$