Question

E that the function g is defined, for all real numbers, as follows.

Answer 1

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.

`\begin{gathered} f(x)=-(x-1)^2+1 \\ f(0)=-(0-1)^2+1 \\ f(0)=-1+1 \\ f(0)=0 \end{gathered}`

02. Finding g(2)

Since 2 ≥ 2, let's use the third equation.

`\begin{gathered} f(x)=(1)/(4)x-2 \\ f(2)=(1)/(4)*2-2 \\ f(2)=(2)/(4)-2 \\ f(2)=(1)/(2)-2 \\ f(2)=(1-4)/(2) \\ f(2)=-(3)/(2) \end{gathered}`

04. Finding g(4)

Since 4 ≥ 2, let's use the third equation.

`\begin{gathered} f(x)=(1)/(4)x-2 \\ f(4)=(1)/(4)*4-2 \\ f(4)=(4)/(4)-2 \\ f(4)=1-2 \\ f(4)=-1 \end{gathered}`

Answer:

`\begin{gathered} f(0)=0 \\ f(2)=-(3)/(2) \\ f(4)=-1 \end{gathered}`