To find the values of [tex]\( f(-4) \)[/tex] and [tex]\( g(7) \)[/tex], we can follow these steps:
1. Calculating [tex]\( f(-4) \)[/tex]:
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[
f(x) = 4x^2 - x
\][/tex]
To find [tex]\( f(-4) \)[/tex], substitute [tex]\( x = -4 \)[/tex] into the function:
[tex]\[
f(-4) = 4(-4)^2 - (-4)
\][/tex]
Simplify the expression inside the function:
[tex]\[
(-4)^2 = 16 \quad \text{(since squaring a negative number gives a positive result)}
\][/tex]
So:
[tex]\[
f(-4) = 4 \cdot 16 + 4
\][/tex]
Multiply and simplify further:
[tex]\[
f(-4) = 64 + 4
\][/tex]
Thus:
[tex]\[
f(-4) = 68
\][/tex]
2. Calculating [tex]\( g(7) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[
g(x) = -4x + 2
\][/tex]
To find [tex]\( g(7) \)[/tex], substitute [tex]\( x = 7 \)[/tex] into the function:
[tex]\[
g(7) = -4 \cdot 7 + 2
\][/tex]
Multiply and simplify:
[tex]\[
-4 \cdot 7 = -28
\][/tex]
So:
[tex]\[
g(7) = -28 + 2
\][/tex]
Thus:
[tex]\[
g(7) = -26
\][/tex]
In conclusion, the values are:
[tex]\[
f(-4) = 68
\][/tex]
[tex]\[
g(7) = -26
\][/tex]
