Answer :
Sure! Let's solve each part of the question, step by step.
### Part 7: Finding [tex]\( g(-12) \)[/tex]
Given the function [tex]\( g(x) = 1 - \frac{3}{4} x \)[/tex], we need to find [tex]\( g(-12) \)[/tex].
1. Substitute [tex]\( x = -12 \)[/tex] into the function:
[tex]\[ g(-12) = 1 - \frac{3}{4} (-12) \][/tex]
2. Calculate the value inside the function:
[tex]\[ g(-12) = 1 - (-9) \][/tex]
3. Simplify:
[tex]\[ g(-12) = 1 + 9 \][/tex]
[tex]\[ g(-12) = 10 \][/tex]
So, [tex]\( g(-12) = 10.0 \)[/tex].
### Part 8: Finding [tex]\( g(0) \)[/tex]
Next, we need to find [tex]\( g(0) \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ g(0) = 1 - \frac{3}{4} (0) \][/tex]
2. Calculate the value inside the function:
[tex]\[ g(0) = 1 - 0 \][/tex]
3. Simplify:
[tex]\[ g(0) = 1 \][/tex]
So, [tex]\( g(0) = 1.0 \)[/tex].
### Part 9: Finding [tex]\( -5 \cdot g(4) -1 \)[/tex]
Finally, we need to find the value of [tex]\( -5 \cdot g(4) - 1 \)[/tex].
1. First, find [tex]\( g(4) \)[/tex] by substituting [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ g(4) = 1 - \frac{3}{4} (4) \][/tex]
2. Calculate the value inside the function:
[tex]\[ g(4) = 1 - 3 \][/tex]
3. Simplify:
[tex]\[ g(4) = -2 \][/tex]
Now substitute this value into the expression [tex]\( -5 \cdot g(4) - 1 \)[/tex]:
4. Substitute [tex]\( g(4) = -2 \)[/tex] into the expression:
[tex]\[ -5 \cdot (-2) - 1 \][/tex]
5. Calculate the value:
[tex]\[ 10 - 1 \][/tex]
6. Simplify:
[tex]\[ 9 \][/tex]
So, [tex]\( -5 \cdot g(4) - 1 = 9.0 \)[/tex].
Therefore, the answers are:
1. [tex]\( g(-12) = 10.0 \)[/tex]
2. [tex]\( g(0) = 1.0 \)[/tex]
3. [tex]\( -5 \cdot g(4) - 1 = 9.0 \)[/tex]
### Part 7: Finding [tex]\( g(-12) \)[/tex]
Given the function [tex]\( g(x) = 1 - \frac{3}{4} x \)[/tex], we need to find [tex]\( g(-12) \)[/tex].
1. Substitute [tex]\( x = -12 \)[/tex] into the function:
[tex]\[ g(-12) = 1 - \frac{3}{4} (-12) \][/tex]
2. Calculate the value inside the function:
[tex]\[ g(-12) = 1 - (-9) \][/tex]
3. Simplify:
[tex]\[ g(-12) = 1 + 9 \][/tex]
[tex]\[ g(-12) = 10 \][/tex]
So, [tex]\( g(-12) = 10.0 \)[/tex].
### Part 8: Finding [tex]\( g(0) \)[/tex]
Next, we need to find [tex]\( g(0) \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ g(0) = 1 - \frac{3}{4} (0) \][/tex]
2. Calculate the value inside the function:
[tex]\[ g(0) = 1 - 0 \][/tex]
3. Simplify:
[tex]\[ g(0) = 1 \][/tex]
So, [tex]\( g(0) = 1.0 \)[/tex].
### Part 9: Finding [tex]\( -5 \cdot g(4) -1 \)[/tex]
Finally, we need to find the value of [tex]\( -5 \cdot g(4) - 1 \)[/tex].
1. First, find [tex]\( g(4) \)[/tex] by substituting [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ g(4) = 1 - \frac{3}{4} (4) \][/tex]
2. Calculate the value inside the function:
[tex]\[ g(4) = 1 - 3 \][/tex]
3. Simplify:
[tex]\[ g(4) = -2 \][/tex]
Now substitute this value into the expression [tex]\( -5 \cdot g(4) - 1 \)[/tex]:
4. Substitute [tex]\( g(4) = -2 \)[/tex] into the expression:
[tex]\[ -5 \cdot (-2) - 1 \][/tex]
5. Calculate the value:
[tex]\[ 10 - 1 \][/tex]
6. Simplify:
[tex]\[ 9 \][/tex]
So, [tex]\( -5 \cdot g(4) - 1 = 9.0 \)[/tex].
Therefore, the answers are:
1. [tex]\( g(-12) = 10.0 \)[/tex]
2. [tex]\( g(0) = 1.0 \)[/tex]
3. [tex]\( -5 \cdot g(4) - 1 = 9.0 \)[/tex]
