Answer:
[tex]\frac{g(x+h)-g(x)}{h}=9[/tex]
Step-by-step explanation:
we have
[tex]g(x)=9x-10[/tex]
To find out g(x+h) substitute the variable x by the variable (x+h) in the function g(x)
so
[tex]g(x+h)=9(x+h)-10[/tex]
[tex]g(x+h)=9x+9h-10[/tex]
Evaluate
[tex]\frac{g(x+h)-g(x)}{h}[/tex]
we have
[tex]g(x+h)=9x+9h-10[/tex]
[tex]g(x)=9x-10[/tex]
substitute in the expression
[tex]\frac{9x+9h-10-(9x-10)}{h}[/tex]
[tex]\frac{9x+9h-10-9x+10)}{h}[/tex]
[tex]\frac{9h}{h}[/tex]
[tex]9[/tex]
therefore
[tex]\frac{g(x+h)-g(x)}{h}=9[/tex]
