Answer :
We are given the function
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2.
$$[/tex]
We need to calculate [tex]$f(-2)$[/tex].
1. Substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2) = 5(-2)^4 - 3(-2)^2 + 6(-2) + 2.
$$[/tex]
2. Calculate each term:
- The first term:
[tex]$$(-2)^4 = 16,$$[/tex]
so
[tex]$$5 \cdot 16 = 80.$$[/tex]
- The second term:
[tex]$$(-2)^2 = 4,$$[/tex]
so
[tex]$$-3 \cdot 4 = -12.$$[/tex]
- The third term:
[tex]$$6 \cdot (-2) = -12.$$[/tex]
- The constant term is [tex]$2$[/tex].
3. Add all the terms together:
[tex]$$
f(-2) = 80 - 12 - 12 + 2.
$$[/tex]
4. Combine the values:
[tex]$$
80 - 12 = 68, \quad 68 - 12 = 56, \quad 56 + 2 = 58.
$$[/tex]
Thus, the final answer is
[tex]$$
f(-2) = 58.
$$[/tex]
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2.
$$[/tex]
We need to calculate [tex]$f(-2)$[/tex].
1. Substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2) = 5(-2)^4 - 3(-2)^2 + 6(-2) + 2.
$$[/tex]
2. Calculate each term:
- The first term:
[tex]$$(-2)^4 = 16,$$[/tex]
so
[tex]$$5 \cdot 16 = 80.$$[/tex]
- The second term:
[tex]$$(-2)^2 = 4,$$[/tex]
so
[tex]$$-3 \cdot 4 = -12.$$[/tex]
- The third term:
[tex]$$6 \cdot (-2) = -12.$$[/tex]
- The constant term is [tex]$2$[/tex].
3. Add all the terms together:
[tex]$$
f(-2) = 80 - 12 - 12 + 2.
$$[/tex]
4. Combine the values:
[tex]$$
80 - 12 = 68, \quad 68 - 12 = 56, \quad 56 + 2 = 58.
$$[/tex]
Thus, the final answer is
[tex]$$
f(-2) = 58.
$$[/tex]
