Question

Given the function, calculate the following:(Shown in image)Round to nearest decimal place as needed. If output doesn’t exist put DNE.

Answer 1

• (a)f(-2)=2.45.

,

• (b) f(-1) = 2.

,

• (c)f(0) = 1.41

,

• (d)f(1) = 0.

,

• (e)f(2)=1.41i. or DNE

Explanation:

Given the function:

`f(x)=√(-2x+2)`

To calculate the given values, replace x with the given value in each case.

(a)f(-2)

`\begin{gathered} f(-2)=√(-2(-2)+2)=√(4+2)=√(6) \\ \implies f(-2)\approx2.45 \end{gathered}`

The value of f(-2) is approximately 2.45.

(b)f(-1)

`\begin{gathered} f(-1)=√(-2(-1)+2)=√(2+2)=√(4)=2 \\ \implies f(-1)=2 \end{gathered}`

The value of f(-1) is 2.

(c)f(0)

`\begin{gathered} f(0)=√(-2(0)+2)=√(0+2)=√(2)\approx1.41 \\ \implies f(0)\approx1.41 \end{gathered}`

The value of f(0) is approximately 1.41

(d)f(1)

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

The value of f(1) is 0.

(e)f(2)

`\begin{gathered} f(2)=√(-2(2)+2)=√(-4+2)=√(-2)=1.41i \\ \implies f(2)=1.41i \end{gathered}`

The value of f(2) is 1.41i.

Since this value is not real, we write DNE for f(2).