Let's go through the problem step-by-step.
The given functions are:
[tex]\[ f(x) = 5x + 2 \][/tex]
[tex]\[ g(x) = 2x^2 - x \][/tex]
We are asked to find [tex]\( f(-7) \)[/tex] and [tex]\( g(-5) \)[/tex].
### Calculating [tex]\( f(-7) \)[/tex]:
1. Substitute [tex]\( x = -7 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-7) = 5(-7) + 2 \][/tex]
2. Simplify the expression inside the function:
[tex]\[ f(-7) = -35 + 2 \][/tex]
3. Combine the terms:
[tex]\[ f(-7) = -33 \][/tex]
So,
[tex]\[ f(-7) = -33 \][/tex]
### Calculating [tex]\( g(-5) \)[/tex]:
1. Substitute [tex]\( x = -5 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(-5) = 2(-5)^2 - (-5) \][/tex]
2. Simplify the squared term and then the entire expression:
[tex]\[ g(-5) = 2(25) + 5 \][/tex]
3. Multiply and add/subtract the necessary values:
[tex]\[ g(-5) = 50 + 5 \][/tex]
4. Combine the terms:
[tex]\[ g(-5) = 55 \][/tex]
So,
[tex]\[ g(-5) = 55 \][/tex]
Hence, the simplified answers are:
[tex]\[ f(-7) = -33 \][/tex]
[tex]\[ g(-5) = 55 \][/tex]
