Given:
[tex]f(x)=\begin{cases}{2x+7\text{ \_\_\_\_}x\leq0} \\ {} \\ {4-x,\text{ \_\_\_\_\_}x>0}\end{cases}[/tex]
Required:
We need to find the value of f(-2), f(0), and f(1),
Explanation:
a)
Let x =-2.
We know that -2 is less than 0.
The function for x =-2 is
[tex]f(x)=2x+7,\text{ }x\leq0[/tex]
Substitute x =-2 in the equation.
[tex]f(-2)=2(-2)+7[/tex][tex]f(-2)=-4+7[/tex][tex]f(-2)=3[/tex]
b)
Let x =0.
[tex]T\text{he values x =0 also includeed in the inequality }x\leq0\text{ , }[/tex]
The function for x =0 is
[tex]f(x)=2x+7[/tex]
Substitute x = 0 in the equation.
[tex]f(0)=2(0)+7[/tex][tex]f(0)=0+7[/tex][tex]f(0)=7[/tex]
c)
Let x =1.
We know that x is greater than 0.
The function for x =1 is
[tex]f(x)=4-x,\text{ x>0}[/tex]
Substitute x =1 in the equaiton.
[tex]f(1)=4-1[/tex][tex]f(1)=3[/tex]
Final answer:
a)
[tex]f(-2)=3[/tex]
b)
[tex]f(0)=7[/tex]
c)
[tex]f(1)=3[/tex]
