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The functions [tex][tex]$f$[/tex][/tex] and [tex][tex]$g$[/tex][/tex] are defined as follows:

[tex]\[ f(x) = 4x^2 - x \][/tex]
[tex]\[ g(x) = -4x + 2 \][/tex]

Find [tex][tex]$f(-4)$[/tex][/tex] and [tex][tex]$g(7)$[/tex][/tex]. Simplify your answers as much as possible.

[tex]\[ f(-4) = \][/tex]
[tex]\[ \square \][/tex]

[tex]\[ g(7) = \][/tex]
[tex]\[ \square \][/tex]



Answer :

GinnyAnswer
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]

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