Answered

Join IDNLearn.com and start getting the answers you've been searching for. Our experts are ready to provide prompt and detailed answers to any questions you may have.

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 :

GinnyAnsweridn
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 contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.