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 $f\left(1\right)$.

• A. 2
• B. 1
• C. 0.0
• D. 3

Answer 1

The correct option is C 0.0

$\text{Given,}f\left(x\right)=\{\begin{array}{c}\sqrt{x-1}\text{if}x\ge 1\\ 2\text{if}x<1\end{array}$
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, 1 lies in the 1st interval. So for x = 1, $f\left(x\right)=\sqrt{x-1}$

$\therefore f\left(1\right)=\sqrt{1-1}=0$