Let's solve the problem step by step.
1. Define the function [tex]\( h(a) \)[/tex]:
[tex]\[ h(a) = 5a + 1 \][/tex]
2. Define the function [tex]\( g(a) \)[/tex]:
[tex]\[ g(a) = 2a - 6 \][/tex]
3. Substitute [tex]\( a = -2 \)[/tex] into [tex]\( h(a) \)[/tex] to find [tex]\( h(-2) \)[/tex]:
[tex]\[ h(-2) = 5(-2) + 1 \][/tex]
First, multiply 5 by -2:
[tex]\[ 5 \times -2 = -10 \][/tex]
Then add 1:
[tex]\[ -10 + 1 = -9 \][/tex]
So, [tex]\( h(-2) = -9 \)[/tex].
4. Substitute [tex]\( a = -2 \)[/tex] into [tex]\( g(a) \)[/tex] to find [tex]\( g(-2) \)[/tex]:
[tex]\[ g(-2) = 2(-2) - 6 \][/tex]
First, multiply 2 by -2:
[tex]\[ 2 \times -2 = -4 \][/tex]
Then subtract 6:
[tex]\[ -4 - 6 = -10 \][/tex]
So, [tex]\( g(-2) = -10 \)[/tex].
5. Find [tex]\( (h - g)(-2) \)[/tex] by subtracting [tex]\( g(-2) \)[/tex] from [tex]\( h(-2) \)[/tex]:
[tex]\[ (h - g)(-2) = h(-2) - g(-2) \][/tex]
Substitute the values:
[tex]\[ (h - g)(-2) = -9 - (-10) \][/tex]
Subtracting a negative number is equivalent to adding its positive:
[tex]\[ -9 - (-10) = -9 + 10 = 1 \][/tex]
Thus, the result is:
[tex]\[ h(-2) = -9 \][/tex]
[tex]\[ g(-2) = -10 \][/tex]
[tex]\[ (h - g)(-2) = 1 \][/tex]
