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The functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex] are defined as follows:

[tex]\[ f(x) = -4x^2 - 3 \][/tex]
[tex]\[ g(x) = 2x - 1 \][/tex]

Find [tex]\( f(5) \)[/tex] and [tex]\( g(-6) \)[/tex]. Simplify your answers as much as possible.

[tex]\[ f(5) = \][/tex]
[tex]\[ \square \][/tex]

[tex]\[ g(-6) = \][/tex]
[tex]\[ \square \][/tex]

Sagot :

GinnyAnswer
To find the values of [tex]\( f(5) \)[/tex] and [tex]\( g(-6) \)[/tex] based on the given functions [tex]\( f(x) = -4x^2 - 3 \)[/tex] and [tex]\( g(x) = 2x - 1 \)[/tex], we follow these steps:

1. Finding [tex]\( f(5) \)[/tex]

Given the function [tex]\( f(x) = -4x^2 - 3 \)[/tex]:
[tex]\[ f(5) = -4(5)^2 - 3 \][/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ f(5) = -4(25) - 3 \][/tex]
Simplify the expression:
[tex]\[ f(5) = -100 - 3 \][/tex]
[tex]\[ f(5) = -103 \][/tex]

So, the value of [tex]\( f(5) \)[/tex] is:
[tex]\[ f(5) = -103 \][/tex]

2. Finding [tex]\( g(-6) \)[/tex]

Given the function [tex]\( g(x) = 2x - 1 \)[/tex]:
[tex]\[ g(-6) = 2(-6) - 1 \][/tex]
Substitute [tex]\( x = -6 \)[/tex]:
[tex]\[ g(-6) = -12 - 1 \][/tex]
Simplify the expression:
[tex]\[ g(-6) = -13 \][/tex]

So, the value of [tex]\( g(-6) \)[/tex] is:
[tex]\[ g(-6) = -13 \][/tex]

Hence, the final results are:
[tex]\[ f(5) = -103 \][/tex]
[tex]\[ g(-6) = -13 \][/tex]
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