Question

Find and simplify a) f(a), b) f(a+h) and c) f(a+h)-f(a)/h, h not equal to 0 using the given function f(x)=x^2+5x-10

Answer 1

attached the equation, since it probably doesn't make sense the way I wrote it.

Answer 2

f(a) means take the expression f(x), and replace all of the xs with as instead. So what does f(a) look like?

Answer 3

so f(x), f(x+h), and f(x+h)-f(x)/h?

Answer 4

I think you're meant to work with f(a) for the most part. If \[f(x)=x^2+5x-10\]then what does \(f(a)\) equal?

Answer 5

x^2+5x-10?

Answer 6

Well that's f(x). If the expression for f(x) has loads of x's in it, then it stands to reason that f(a) will have loads of a's in it.

Answer 7

I'm confused.. How can I find what f(a) equals?

Answer 8

Anywhere there's an 'x' in f(x), you just replace them with an 'a' in f(a).

Answer 9

Look at it this way ... if you want to compute f(7), it means you put 7 every place there was an x. So similarly, f(a) means you put an 'a' everywhere there was an 'x'. Just change all the 'x' to 'a'.

Answer 10

so f(a)=a^2+5(a)-10?

Answer 11

yep

Answer 12

Bingo! Now do the same thing again, but this time, instead of putting an 'a' everywhere, put (a+h) everywhere. It's exactly the same, (a+h) is just a number, like any other.

Answer 13

f(a+h)=(a+h)^2+5(a+h)-10

Answer 14

Yep yep! Now here's the tricky part: Start with f(a+h), take away f(a), and divide it all by h:\[\frac{f(a+h)-f(a)}{h}\]

Answer 15

How do I do that?

Answer 16

You already know what f(a+h) is, and you know what f(a) is. All you do is put them in that formula.

Answer 17

I'm still confused

Answer 18

Alrighty. If I tell you that \[y=17\]and\[x=3\], then I ask you to tell me what the value of \[x+y\], what would you calculate to be the answer?

Answer 19

20

Answer 20

Exactly. What you did was say that \[x+y=3+17=20\] right?

Well the situation as we have it now is:
\[f(a)=a^2+5(a)-10\]\[f(a+h)=(a+h)^2+5(a+h)-10\]\[h=h\]

Now instead of the expression x+y, the expression is \[\frac{f(a+h)-f(a)}{h}\]

Answer 21

oh okay, I think I got it now

Answer 22

Any progress?