Answer :
We are given the function
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2.
$$[/tex]
To find [tex]$f(-2)$[/tex], we substitute [tex]$x = -2$[/tex] into the function:
1. Compute the first term:
[tex]$$
5(-2)^4.
$$[/tex]
Since
[tex]$$
(-2)^4 = 16,
$$[/tex]
then
[tex]$$
5 \times 16 = 80.
$$[/tex]
2. Compute the second term:
[tex]$$
-3(-2)^2.
$$[/tex]
Since
[tex]$$
(-2)^2 = 4,
$$[/tex]
then
[tex]$$
-3 \times 4 = -12.
$$[/tex]
3. Compute the third term:
[tex]$$
6(-2) = -12.
$$[/tex]
4. The constant term remains:
[tex]$$
2.
$$[/tex]
Now, add all the terms together:
[tex]$$
f(-2) = 80 + (-12) + (-12) + 2.
$$[/tex]
Calculate the sum step-by-step:
- [tex]$80 - 12 = 68$[/tex],
- [tex]$68 - 12 = 56$[/tex],
- [tex]$56 + 2 = 58$[/tex].
Thus, the value of [tex]$f(-2)$[/tex] is
[tex]$$
\boxed{58}.
$$[/tex]
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2.
$$[/tex]
To find [tex]$f(-2)$[/tex], we substitute [tex]$x = -2$[/tex] into the function:
1. Compute the first term:
[tex]$$
5(-2)^4.
$$[/tex]
Since
[tex]$$
(-2)^4 = 16,
$$[/tex]
then
[tex]$$
5 \times 16 = 80.
$$[/tex]
2. Compute the second term:
[tex]$$
-3(-2)^2.
$$[/tex]
Since
[tex]$$
(-2)^2 = 4,
$$[/tex]
then
[tex]$$
-3 \times 4 = -12.
$$[/tex]
3. Compute the third term:
[tex]$$
6(-2) = -12.
$$[/tex]
4. The constant term remains:
[tex]$$
2.
$$[/tex]
Now, add all the terms together:
[tex]$$
f(-2) = 80 + (-12) + (-12) + 2.
$$[/tex]
Calculate the sum step-by-step:
- [tex]$80 - 12 = 68$[/tex],
- [tex]$68 - 12 = 56$[/tex],
- [tex]$56 + 2 = 58$[/tex].
Thus, the value of [tex]$f(-2)$[/tex] is
[tex]$$
\boxed{58}.
$$[/tex]
