Question

Find the functional values g(-1), g(0), and g(4) for the compound function.

g(x)= {7 if x is less than or equal to 0} {1/x if x>0}

Answer 1

Find the functional value $g(-1), g(0), g(4)$ for the compound function

$$g(x) = \begin{cases} 7, & x \leq 0 \\ \frac{1}{x}, & x \geq 0 \end{cases}$$

Solution

$$\begin{aligned} x &= -1 \quad & \Rightarrow \quad g(x) = 7 \quad & \Rightarrow \quad g(-1) = 7 \\ x &= 0 \quad & \Rightarrow \quad g(x) = 7 \quad & \Rightarrow \quad g(0) = 7 \\ x &= 4 \quad & \Rightarrow \quad g(x) = \frac{1}{x} \quad & \Rightarrow \quad g(4) = \frac{1}{4} \end{aligned}$$

Answer: $g(-1) = 7$, $g(0) = 7$, $g(4) = \frac{1}{4}$.