Answer :

To evaluate the function [tex]\( f(x) = x^4 - 7x^2 + 23 \)[/tex] at [tex]\( x = -2 \)[/tex], follow these steps:

1. Substitute [tex]\(-2\)[/tex] for [tex]\(x\)[/tex] in the function:
[tex]\[
f(-2) = (-2)^4 - 7(-2)^2 + 23
\][/tex]

2. Calculate each term individually:
- [tex]\((-2)^4\)[/tex] is calculated by multiplying [tex]\(-2\)[/tex] by itself four times:
[tex]\[
(-2) \times (-2) \times (-2) \times (-2) = 16
\][/tex]

- [tex]\((-2)^2\)[/tex] is calculated by multiplying [tex]\(-2\)[/tex] by itself:
[tex]\[
(-2) \times (-2) = 4
\][/tex]
Then multiply by [tex]\(-7\)[/tex]:
[tex]\[
-7 \times 4 = -28
\][/tex]

3. Put these values back into the function:
[tex]\[
f(-2) = 16 - 28 + 23
\][/tex]

4. Simplify the expression:
- First, sum 16 and [tex]\(-28\)[/tex]:
[tex]\[
16 - 28 = -12
\][/tex]
- Finally, add 23 to [tex]\(-12\)[/tex]:
[tex]\[
-12 + 23 = 11
\][/tex]

Therefore, the result of [tex]\( f(-2) \)[/tex] is [tex]\( 11 \)[/tex].

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Rewritten by : Barada