Question

Evaluate the function at each specified value of the independent variable and simplify. (Question is in the photo sorry lol)

Answer 1

Given:

`f(x)=\begin{cases}{2x+7\text{ \_\_\_\_}x\leq0} \\ {} \\ {4-x,\text{ \_\_\_\_\_}x>0}\end{cases}`

Required:

We need to find the value of f(-2), f(0), and f(1),

Step-by-step explanation:

a)

Let x =-2.

We know that -2 is less than 0.

The function for x =-2 is

`f(x)=2x+7,\text{ }x\leq0`

Substitute x =-2 in the equation.

`f(-2)=2(-2)+7`
`f(-2)=-4+7`
`f(-2)=3`

b)

Let x =0.

The function for x =0 is

`f(x)=2x+7`

Substitute x = 0 in the equation.

`f(0)=2(0)+7`
`f(0)=0+7`
`f(0)=7`

c)

Let x =1.

We know that x is greater than 0.

The function for x =1 is

`f(x)=4-x,\text{ x>0}`

Substitute x =1 in the equaiton.

`f(1)=4-1`
`f(1)=3`

Final answer:

a)

`f(-2)=3`

b)

`f(0)=7`

c)

`f(1)=3`