SOLUTION: Let f(x) = 5x + 4. Find f(x) - f(a) / x-a, if x does not equal a.

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Question 823685: Let f(x) = 5x + 4. Find f(x) - f(a) / x-a, if x does not equal a.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, there--

YOUR PROBLEM:
Let f(x) = 5x + 4. Find f(x) - f(a) / x-a, if x does not equal a.

SOLUTION:
f(x) = 5x + 4
f(a) = 5a + 4

Now we fill these values in to the expression you are asked to find
[f(x) - f(a)]/(x-a) = [(5x-4) - (5a-4)] / (x-a)

Simplify.
[f(x) - f(a)]/(x-a) = [5x - 4 - 5a + 4]/(x-a)
[f(x) - f(a)]/(x-a) = [5x - 5a]/(x-a)

Factor a 5 from the expression in the numerator.
[f(x) - f(a)]/(x-a) = [(5)(x - a]/(x-a)

Notice that the numerator and denominator both contain the factor x-a. They cancel out, and we are left with
[f(x) - f(a)]/(x-a) = 5

Something interesting to notice and wonder about :: Look at your original function.
f(x) = 5x - 4

Do you see why 5 is the correct answer to your problem? 

Good luck,
Mrs.Figgy