Answer :
Sure! Let's evaluate the function [tex]\( f(x) = x^4 - 7x^2 + 23 \)[/tex] at [tex]\( x = -2 \)[/tex].
1. Substitute [tex]\(-2\)[/tex] into the function:
The function is given by [tex]\( f(x) = x^4 - 7x^2 + 23 \)[/tex]. We will substitute [tex]\( x = -2 \)[/tex] into this expression.
2. Calculate [tex]\( (-2)^4 \)[/tex]:
[tex]\[ (-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16 \][/tex]
So, [tex]\( (-2)^4 = 16 \)[/tex].
3. Calculate [tex]\( 7 \times (-2)^2 \)[/tex]:
First, find [tex]\( (-2)^2 \)[/tex]:
[tex]\[ (-2)^2 = (-2) \times (-2) = 4 \][/tex]
Then, multiply by 7:
[tex]\[ 7 \times 4 = 28 \][/tex]
4. Plug these values into the function:
Substitute these into the expression for [tex]\( f(x) \)[/tex]:
[tex]\[ f(-2) = 16 - 28 + 23 \][/tex]
5. Simplify the expression:
[tex]\[ 16 - 28 = -12 \][/tex]
Then add 23:
[tex]\[ -12 + 23 = 11 \][/tex]
Therefore, [tex]\( f(-2) = 11 \)[/tex].
1. Substitute [tex]\(-2\)[/tex] into the function:
The function is given by [tex]\( f(x) = x^4 - 7x^2 + 23 \)[/tex]. We will substitute [tex]\( x = -2 \)[/tex] into this expression.
2. Calculate [tex]\( (-2)^4 \)[/tex]:
[tex]\[ (-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16 \][/tex]
So, [tex]\( (-2)^4 = 16 \)[/tex].
3. Calculate [tex]\( 7 \times (-2)^2 \)[/tex]:
First, find [tex]\( (-2)^2 \)[/tex]:
[tex]\[ (-2)^2 = (-2) \times (-2) = 4 \][/tex]
Then, multiply by 7:
[tex]\[ 7 \times 4 = 28 \][/tex]
4. Plug these values into the function:
Substitute these into the expression for [tex]\( f(x) \)[/tex]:
[tex]\[ f(-2) = 16 - 28 + 23 \][/tex]
5. Simplify the expression:
[tex]\[ 16 - 28 = -12 \][/tex]
Then add 23:
[tex]\[ -12 + 23 = 11 \][/tex]
Therefore, [tex]\( f(-2) = 11 \)[/tex].
