Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Use the function [tex]f(x) = 2x^3 - 3x^2 + 7[/tex] to complete the exercises.

[tex]\[
\begin{array}{l}
f(-1) = \hat{v} \\
f(1) = \hat{v} \\
f(2) = \hat{\imath}
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To evaluate the function [tex]\( f(x) = 2x^3 - 3x^2 + 7 \)[/tex] at the specified points, follow these steps:

### 1. Calculate [tex]\( f(-1) \)[/tex]:
Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 2(-1)^3 - 3(-1)^2 + 7 \][/tex]

Now evaluate this expression:
- [tex]\((-1)^3 = -1\)[/tex]
- [tex]\((-1)^2 = 1\)[/tex]
- [tex]\(2 \times (-1) = -2\)[/tex]
- [tex]\(3 \times 1 = 3\)[/tex]

Thus:
[tex]\[ f(-1) = 2(-1) - 3(1) + 7 \][/tex]
[tex]\[ f(-1) = -2 - 3 + 7 \][/tex]
[tex]\[ f(-1) = 2 \][/tex]

So, [tex]\( f(-1) = 2 \)[/tex].

### 2. Calculate [tex]\( f(1) \)[/tex]:
Substitute [tex]\( x = 1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(1) = 2(1)^3 - 3(1)^2 + 7 \][/tex]

Now evaluate this expression:
- [tex]\((1)^3 = 1\)[/tex]
- [tex]\((1)^2 = 1\)[/tex]
- [tex]\(2 \times 1 = 2\)[/tex]
- [tex]\(3 \times 1 = 3\)[/tex]

Thus:
[tex]\[ f(1) = 2(1) - 3(1) + 7 \][/tex]
[tex]\[ f(1) = 2 - 3 + 7 \][/tex]
[tex]\[ f(1) = 6 \][/tex]

So, [tex]\( f(1) = 6 \)[/tex].

### 3. Calculate [tex]\( f(2) \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(2) = 2(2)^3 - 3(2)^2 + 7 \][/tex]

Now evaluate this expression:
- [tex]\((2)^3 = 8\)[/tex]
- [tex]\((2)^2 = 4\)[/tex]
- [tex]\(2 \times 8 = 16\)[/tex]
- [tex]\(3 \times 4 = 12\)[/tex]

Thus:
[tex]\[ f(2) = 2(8) - 3(4) + 7 \][/tex]
[tex]\[ f(2) = 16 - 12 + 7 \][/tex]
[tex]\[ f(2) = 11 \][/tex]

So, [tex]\( f(2) = 11 \)[/tex].

### Summary:
[tex]\[ \begin{array}{l} f(-1) = 2 \\ f(1) = 6 \\ f(2) = 11 \end{array} \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.