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Si [tex]$f(x) = 3x^2 - 4x + 2$[/tex], ¿cuánto es [tex]$f(-2)$[/tex]?

A. [tex]-18[/tex]
B. [tex]-2[/tex]
C. [tex]6[/tex]
D. [tex]22[/tex]
E. [tex]46[/tex]

Answer :

To solve the problem, we need to find the value of the function [tex]\( f(x) = 3x^2 - 4x + 2 \)[/tex] at [tex]\( x = -2 \)[/tex].

Here is a step-by-step solution:

1. Substitute [tex]\( x = -2 \)[/tex] into the function:
We need to replace [tex]\( x \)[/tex] with [tex]\(-2\)[/tex] in the function.
[tex]\[
f(-2) = 3(-2)^2 - 4(-2) + 2
\][/tex]

2. Calculate [tex]\((-2)^2\)[/tex]:
[tex]\((-2)^2 = 4\)[/tex]

3. Multiply by 3:
[tex]\(3 \times 4 = 12\)[/tex]

4. Calculate [tex]\(-4 \times (-2)\)[/tex]:
[tex]\(-4 \times (-2) = 8\)[/tex]

5. Add all parts together:
[tex]\[
f(-2) = 12 + 8 + 2
\][/tex]

6. Final calculation:
[tex]\(12 + 8 = 20\)[/tex]
[tex]\(20 + 2 = 22\)[/tex]

Therefore, the value of [tex]\( f(-2) \)[/tex] is [tex]\( \boxed{22} \)[/tex].

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