Question 36340This question is from textbook Algebra and Trigonometry with Analytic Geometry
: I usually give the work that I've done to make sure I did it right, but in this case, I don't know where to begin. Here goes...
If f(x)=x^2 + 5, find f(a + h) - (a)
Thank you.
This question is from textbook Algebra and Trigonometry with Analytic Geometry
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! Okay, this is just a confusing concept if you haven't had much exposure to it. Usually we see functions of the form f(x)=2x, or something like that. This is read "f of x equals two x." So, in this case, if we were asked for f(a), we would say f(a)=2a, read "f of a equals two a." Note, we simply plugged in the new value in parenthesis where the x was originally.
So in your question, let's take it in steps.
First, we can do the easiest part, f(a) (I'm guessing you meant f(a), not just (a)). f(a)=a^2+5.
Now, f(a+h)=(a+h)^2+5 = a^2+2ah+h^2+5.
Finally, subtracting the two gives:
f(a+h)-f(a) = (a^2+2ah+h^2+5)-(a^2+5) = a^2+2ah+h^2+5-a^2-5 = 2ah+h^2
So the answer is 2ah+h^2.
(If it was really (a), not f(a), it would jsut be (a^2+2ah+h^2+5)-(a) = a^2+2ah+h^2+5-a.)
Just by the way, this is the beginning of calculus:).
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