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]
