Question

Determining a function! need help understanding this problem!

Answer 1

@cwrw238 hey! you have helped me before, would you happen to be able to run me through the steps to solve this problem?

Answer 2

or @Directrix , you have helped me before as well. :)

Answer 3

f(x) = x^2 + 5x

What is f(a + h) ?

Substitute (a + h) in place of x in f(x)

f(a + h) = ( a + h) ^2 + 5* (a + h)

Crank this out and simplify:

( a + h) ^2 + 5* (a + h) =

Answer 4

okay so i would get a^2+2ah+h^2+5a+h

Answer 5

what would i do after this?

Answer 6

There's an error here: ... +5a+h

Answer 7

Check your work.

Answer 8

oh +5a+5h

Answer 9

so once i have that what do i have to do? sorry i have to leave in 5 minutes so i am trying to finish this up quick!

Answer 10

Now, find f(a) where f(x) = x^2 + 5x

In place of x, write a to determine f(a).

Post what you get. Then, we'll put the two pieces of the problem together and crank out an answer.

Answer 11

okay thank you! i have to go now but i will get back on later to finish the problem.

Answer 12

Okay.

Answer 13

okay i am back! one second let me look at what you had said above.

Answer 14

im a little confused, but am i just substituting a for x in f(x)=x^2+5x? @Directrix

Answer 15

@xapproachesinfinity hey! would you be able to help?

Answer 16

@jim_thompson5910 hey could you help with the rest of this problem from where directrix left off? he isnt online and i need to finish this problem.

Answer 17

hopefully you found that

f(a) = a^2 + 5a

right?

Answer 18

yes i have that, just not sure what to do with it now!

Answer 19

you have f(a+h) and you have f(a)

subtract the two and tell me what you get

Answer 20

subtract the two things i found earlier? so i would subtract a^2+2ah+h^2+5a+5h-a^2+5a

Answer 21

you subtract like this

Answer 22

f(a+h) - f(a)

[ f(a+h) ] - [ f(a) ]

[ a^2+2ah+h^2+5a+5h ] - [ a^2+5a ]

a^2+2ah+h^2+5a+5h - a^2 - 5a ... notice the sign change

Answer 23

You use brackets or parenthesis to group the two things you are subtracting

you subtract ALL of f(a) from ALL of f(a+h)

Answer 24

ah okay i see. so now i would just simplify?

Answer 25

yes and you get what?

Answer 26

simplified it would be 2ah+5h+h^2?

Answer 27

yes

Answer 28

recall that this is all over h

Answer 29

so this means

\[\Large \frac{f(a+h)-f(a)}{h} = \frac{2ah+5h+h^2}{h}\]

Answer 30

what's next?

Answer 31

would you pull a h from the top?

Answer 32

im not entirely sure

Answer 33

yes you have a common factor of h up top, so factor it out

we factor it out so it will cancel out with the h down below

Answer 34

okay so in factoring out an h do you end up with 2a+5+h?

Answer 35

and in that case the answer would be C

Answer 36

\[\Large \frac{f(a+h)-f(a)}{h} = \frac{2ah+5h+h^2}{h}\]

\[\Large \frac{f(a+h)-f(a)}{h} = \frac{h(2a+5+h)}{h}\]

\[\Large \frac{f(a+h)-f(a)}{h} = \frac{\cancel{h}(2a+5+h)}{\cancel{h}}\]

\[\Large \frac{f(a+h)-f(a)}{h} = 2a+5+h\]

\[\Large \frac{f(a+h)-f(a)}{h} = 2a+h+5\]

so yep, it's C

Answer 37

awesome, thank you very much!

Answer 38

no problem