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

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) (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

RELATED QUESTIONS
Let f(x)=9+x+x ^2 and h not equal to 0. a. is f(8+1) = f(8)+f(1)? Yes or No (I... (answered by solver91311)

If f(x)=3x²+5x-2,find... (answered by Edwin McCravy)

Let f be a linear function. If f(−3) = 7and f(2) = −13,find... (answered by scott8148)

Let f(x) = Ax + B and g(x) = Bx + A, where A does not equal B. If f(g(x)) - g(f(x)) = B - (answered by Fombitz)

Let f(x)=2x^2-5x and find: A: f(-2) B: f(0) C: 2f(x) D:... (answered by jim_thompson5910)

Given f(x) = �5x � 1, find f(a �... (answered by Nate)

Given f(x)=5x-5, find... (answered by mala_kumarkos@yahoo.com)

Given f(x)=-5x-1, find... (answered by edjones)

If f(x) = 5x � 1 find following... (answered by AnlytcPhil)