To solve this question, follow the steps below:
a) Find the function in which the x-value is defined
b) Substitute the function by the value of x and find f(x).
01. Finding g(0)
Since -2 < 0 < 2, let's use the second equation.
[tex]\begin{gathered} f(x)=-(x-1)^2+1 \\ f(0)=-(0-1)^2+1 \\ f(0)=-1+1 \\ f(0)=0 \end{gathered}[/tex]
02. Finding g(2)
Since 2 ≥ 2, let's use the third equation.
[tex]\begin{gathered} f(x)=\frac{1}{4}x-2 \\ f(2)=\frac{1}{4}*2-2 \\ f(2)=\frac{2}{4}-2 \\ f(2)=\frac{1}{2}-2 \\ f(2)=\frac{1-4}{2} \\ f(2)=-\frac{3}{2} \end{gathered}[/tex]
04. Finding g(4)
Since 4 ≥ 2, let's use the third equation.
[tex]\begin{gathered} f(x)=\frac{1}{4}x-2 \\ f(4)=\frac{1}{4}*4-2 \\ f(4)=\frac{4}{4}-2 \\ f(4)=1-2 \\ f(4)=-1 \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} f(0)=0 \\ f(2)=-\frac{3}{2} \\ f(4)=-1 \end{gathered}[/tex]
