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

Answer:

• (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:

$f(x)=\sqrt{-2x+2}$

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

(a)f(-2)

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

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

(b)f(-1)

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

The value of f(-1) is 2.

(c)f(0)

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

The value of f(0) is approximately 1.41

(d)f(1)

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

The value of f(1) is 0.

(e)f(2)

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

The value of f(2) is 1.41i.

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