College Algebra

[rx2023]

This is a question I've come across in my math class homework. I haven't been in a math class since sophomore year of high school due to a brain injury and losing a lot of my math ability. I don't know how to do problems like this anymore so I would appreciate the help and explanation. Thank you!

 

[tkhunny]

g(x) = 7x - 1

g(2) = 7(2) - 1

g(y+5) = 7(y+5) - 1

g(fred) = 7(fred) - 1

 

[JeffM]

This is an introductory problem for differential calculus.

[MATH]g(x) = 7x - 1.[/MATH]
[MATH]g(x + h) = 7(x + h) - 1 = 7x + 7h - 1 = 7x - 1 + 7h.[/MATH]
OK TO HERE? If not, think carefully about tkhunny's post.

[MATH]\therefore g(x + g) - g(x) = 7x - 1 + 7h - (7x - 1) = (7x - 1) - (7x - 1) + 7h = 7h.[/MATH]
Just a simple subtraction and simplification.

[MATH]\therefore h \ne 0 \implies \dfrac{g(x + h) - g(x)}{h} = \dfrac{7h}{h} = 7.[/MATH]