Questions: A function (f) is given below. [ f(x)=leftbeginarraycc x^2+3 text if x leq 0 frac1x text if x>0 endarrayright. ] Find the values of (f(2)), (f(0)), (fleft(frac32right))

$A function (f) is given below. [ f(x)=leftbeginarraycc x^2+3 text if x leq 0 frac1x text if x>0 endarrayright. ] Find the values of (f(2)), (f(0)), (fleft(frac32right))$

Transcript text: A function $f$ is given below. \[ \mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc} x^{2}+3 & \text { if } x \leq 0 \\ \frac{1}{x} & \text { if } x>0 \end{array}\right. \] Find the values of $f(2)$ \[ f(0) \] \[ f\left(\frac{3}{2}\right) \]

Solution

Solution Steps

Step 1: Evaluate $ f(2) $

The function $ f(x) $ is defined as a piecewise function. For $ x > 0 $, the function is given by $ f(x) = \frac{1}{x} $. Since $ 2 > 0 $, we use this part of the function:

\[ f(2) = \frac{1}{2} \]

Step 2: Evaluate $ f(0) $

For $ x \leq 0 $, the function is given by $ f(x) = x^2 + 3 $. Since $ 0 \leq 0 $, we use this part of the function:

\[ f(0) = 0^2 + 3 = 3 \]

Step 3: Evaluate $ f\left(\frac{3}{2}\right) $

For $ x > 0 $, the function is given by $ f(x) = \frac{1}{x} $. Since $ \frac{3}{2} > 0 $, we use this part of the function:

\[ f\left(\frac{3}{2}\right) = \frac{1}{\frac{3}{2}} = \frac{2}{3} \]