Question

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

• A. -1
• B. $\sqrt{-1}$
• C. 0
• D. 2

Answer 1

The correct option is D 2

$\text{Given,}f\left(x\right)=\{\begin{array}{c}\sqrt{x-1}\text{if}x\ge 1\\ 2\text{if}x<1\end{array}$
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, $f\left(x\right)=2$

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