Question

Let g(x)=9x−10 and evaluate g(x+h)−g(x)/h

Answer 1

Answer:

$\frac{g(x+h)-g(x)}{h}=9$

Step-by-step explanation:

we have

$g(x)=9x-10$

To find out g(x+h) substitute the variable x by the variable (x+h) in the function g(x)

so

$g(x+h)=9(x+h)-10$

$g(x+h)=9x+9h-10$

Evaluate

$\frac{g(x+h)-g(x)}{h}$

we have

$g(x+h)=9x+9h-10$

$g(x)=9x-10$

substitute in the expression

$\frac{9x+9h-10-(9x-10)}{h}$

$\frac{9x+9h-10-9x+10)}{h}$

$\frac{9h}{h}$

$9$

therefore

$\frac{g(x+h)-g(x)}{h}=9$