Let's solve the given problem step by step for each part.
### Given:
The function [tex]\( g(x) = 7x + 3 \)[/tex]
### Part (a): [tex]\( g(0) \)[/tex]
We need to find the value of the function when [tex]\( x = 0 \)[/tex].
[tex]\[ g(0) = 7(0) + 3 = 0 + 3 = 3 \][/tex]
So,
[tex]\[ g(0) = 3 \][/tex]
### Part (b): [tex]\( g(3) \)[/tex]
We need to find the value of the function when [tex]\( x = 3 \)[/tex].
[tex]\[ g(3) = 7(3) + 3 = 21 + 3 = 24 \][/tex]
So,
[tex]\[ g(3) = 24 \][/tex]
### Part (c): [tex]\( g\left(\frac{6}{7}\right) \)[/tex]
We need to find the value of the function when [tex]\( x = \frac{6}{7} \)[/tex].
[tex]\[ g\left(\frac{6}{7}\right) = 7 \left( \frac{6}{7} \right) + 3 = 6 + 3 = 9 \][/tex]
So,
[tex]\[ g\left(\frac{6}{7}\right) = 9 \][/tex]
### Part (d): [tex]\( g(-8b) \)[/tex]
We need to find the value of the function when [tex]\( x = -8 \)[/tex].
[tex]\[ g(-8) = 7(-8) + 3 = -56 + 3 = -53 \][/tex]
So,
[tex]\[ g(-8) = -53 \][/tex]
### Part (e): [tex]\( g(b+7) \)[/tex]
We need to find the value of the function when [tex]\( x = 8 + 7 \)[/tex].
[tex]\[ g(15) = 7(15) + 3 = 105 + 3 = 108 \][/tex]
So,
[tex]\[ g(15) = 108 \][/tex]
### Summary of Results:
a. [tex]\( g(0) = 3 \)[/tex]
b. [tex]\( g(3) = 24 \)[/tex]
c. [tex]\( g\left(\frac{6}{7}\right) = 9 \)[/tex]
d. [tex]\( g(-8) = -53 \)[/tex]
e. [tex]\( g(15) = 108 \)[/tex]
