Question

Given the function f(x)={4x+7 if x<0 6x+4 if x>0 _

Answer 1

Given:

`f(x)=\begin{cases}4x+7ifx<0{} \\ 6x+4ifx\ge0{}\end{cases}`

Required:

To find the value of f(-8), f(0), f(4), and f(-100)+f(100).

Step-by-step explanation:

f(-8) :

Clearly -8<0,

So

`\begin{gathered} f(x)=4x+7 \\ f(-8)=4(-8)+7 \\ =-32+7 \\ =-25 \end{gathered}`

f(0) :

Clearly 0=0,

`\begin{gathered} f(x)=6x+4 \\ =6(0)+4 \\ =4 \end{gathered}`

f(4) :

Clearly 4>0,

`\begin{gathered} f(x)=6x+4 \\ f(4)=6(4)+4 \\ =24+4 \\ =28 \end{gathered}`

f(-100)+f(100) :

-100<0

`\begin{gathered} f(x)=4x+7 \\ f(-100)=4(-100)+7 \\ =-400+7 \\ =-393 \end{gathered}`

100>0

`\begin{gathered} f(x)=6x+4 \\ f(100)=6(100)+4 \\ =600+4 \\ =604 \end{gathered}`
`\begin{gathered} f(-100)+f(100)=-393+604 \\ \\ =211 \end{gathered}`

Final Answer:

`\begin{gathered} f(-8)=-25 \\ \\ f(0)=4 \\ \\ f(4)=28 \\ \\ f(-100)+f(100)=211 \end{gathered}`