Question

If  \[f\left( x \right) = \begin{cases}x^2 , & \text{ when }  x < 0 \\ x, & \text{ when }  0 \leq x < 1 \\ \frac{1}{x}, & \text{ when }  x \geq 1\end{cases}\]

find: (a) f(1/2), (b) f(−2), (c) f(1), (d)

\[f\left( \sqrt{3} \right)\] and (e) \[f\left( \sqrt{- 3} \right)\]

 

Answer 1

Given:

\[f\left( x \right) = \begin{cases}x^2 , & \text{ when }  x < 0 \\ x, & \text{ when }  0 \leq x < 1 \\ \frac{1}{x}, & \text{ when }  x \geq 1\end{cases}\] 

Now,
(a) \[f\left( \frac{1}{2} \right) = \frac{1}{2}\]         [ Using f (x) = x, 0 ≤ x < 1]

(b) f ( -2) = ( - 2)² = 4  

(c) \[f\left( 1 \right) = \frac{1}{1} = 1\]

(d) \[f\left( \sqrt{3} \right) = \frac{1}{\sqrt{3}}\]

(e)  \[f\left( \sqrt{- 3} \right)\] Since x is not defined in R,

\[f\left( \sqrt{- 3} \right)\]  does not exist.