Find The Difference Quotient With Funtions

[blitzer]

I'm not sure about a few of these problems or how to pursue them. I have never had trouble with functions until now.

Find the difference quotient

f(x+h)-f(x) / h

and simplify your answer

1. f(x) = 3x - 4
2. f(x) = 1 - x^2

The only way I see to do anything is to plug in the two functions for f(x) in the numerator...but that still leaves me with f(x+h) and the h in the denominator and if I am correct, I don't know what to do next.

 

[Deleted member 4993]

I'm not sure about a few of these problems or how to pursue them. I have never had trouble with functions until now.

Find the difference quotient

f(x+h)-f(x) / h

and simplify your answer

1. f(x) = 3x - 4
2. f(x) = 1 - x^2

The only way I see to do anything is to plug in the two functions for f(x) in the numerator...but that still leaves me with f(x+h) and the h in the denominator and if I am correct, I don't know what to do next.

If

f(x) = 3x - 4

f(x+h) = 3(x+h) - 4

Now find [f(x+h) - f(x)] and continue.....

Please show your work, and exactly where you are stuck - so that we know where to begin to help you.

 

[fasteddie65]

Let's look at f(x) = 1 + x^2.

f(x + h) - f(x) = [1 + (x + h)^2] - (1 + x^2) = 1 + x^2 + 2hx + h^2 - 1 - x^2 = 2hx + h^2

So, [f(x + h) - f(x)]/h = (2hx + h^2)/h = 2x + h