Solution:
The equation for the function is given below as
[tex]g(x)=3-8x[/tex]
Step 1:
Substitute the value of g(x)=0 in the equation above
[tex]\begin{gathered} g(x)=3-8x \\ 0=3-8x \\ 8x=3 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{3}{8} \\ x=\frac{3}{8} \end{gathered}[/tex]
Step 2:
Substitute the value of x=0 in the equation below
[tex]\begin{gathered} g(x)=3-8x \\ g(x)=3-8(0) \\ g(x)=3 \end{gathered}[/tex]
Step 3:
Substitute the value of g(x) =-5
[tex]\begin{gathered} g(x)=3-8x \\ -5=3-8x \\ -5-3=-8x \\ -8=-8x \\ \text{divide both sides by -8} \\ \frac{-8x}{-8}=-\frac{8}{-8} \\ x=1 \end{gathered}[/tex]
Step 4:
Substitute the value of x=3 in the equation below
[tex]\begin{gathered} g(x)=3-8x \\ g(x)=3-8(3) \\ g(x)=3-24 \\ g(x)=-21 \end{gathered}[/tex]
Hence,
The final answer is
