Trouble with f(x)

[witlesswiz]

I am having difficulty understanding f(x) problems. Simple ones I understand but, cannot locate any detail how to's on:

f(x+h)-f(x)
h

if f(x)=11x-4

would I not substitute 11x-4 anywhere I see x?
I keep coming up with f as a final answer and the book has a number answer.

Lost in translation

 

[pka]

If f(x)=11x-4 then f(x+h)=11(x+h)-4=11x+11h-4.
Then f(x+h)-f(x)=(11x+11h-4)-(11x-4).
Now you finish your problem.

 

[witlesswiz]

Mind is not working....I am confused on what you are subbing in the f(x+h) part. Why am I splitting up my f(x)=11x-4

f(x+h)-f(x) divided by h

 

[pka]

Here is a quick lesson in function notation.
If f(x)=x<SUP>2</SUP>-3x+4 then:
f(-2)=(-2)<SUP>2</SUP>-3(-2)+4
f(y)=(y)<SUP>2</SUP>-3(y)+4
f(h)=(h)<SUP>2</SUP>-3(h)+4
f(-3k)=(-3k)<SUP>2</SUP>-3(-3k)+4
f(x+h)=(x+h)<SUP>2</SUP>-3(x+h)+4=(x<SUP>2</SUP>+2xh+h<SUP>2</SUP>)-(3x+3h)-4.

  [11(x+h)-4]-[11x-4]
--------------------------= 11
              h

 

[soroban]

Hello, witlesswiz!

It seems that you don't understand "functions" at all . . .

Given: . f(x) .= .3x + 1

Then f(4) means "let x = 4 in the function".
. . So we have: . f(4) .= .3(4) + 1 .= .13

And f(a + 1) means "let x = a+1 in the function".
. . So we have: . f(a+1) .= .3(a+1) + 1 .= .3a + 4

So f(x+h) means "let x = x+h in the function".
. . So we have: . f(x+h) .= .3(x+h) + 1 .= .3x + 3h + 1

I am having difficulty understanding f(x) problems.
Simple ones I understand, but cannot locate any detail how to's on:

. . . .f(x+h) - f(x)
. . . --------------- . . if f(x) = 11x - 4
. . . . . . .h

I keep coming up with f as a final answer . . . . how?

That strange fraction is called the Difference Quotient.

It is a "recipe" for getting a particular expression.
. . There are three steps to follow . . .

Step 1: . Find f(x + h) . . . replace x with x + h (and simplify)

Step 2: . Subtract f(x) . . . subtract the original function (and simplify)

Step 3: . Divide by h . . . . factor and cancel


Let's try it with: . f(x) .= .11x - 4

Step 1: . f(x + h) . = . 11(x + h) - 4 . = . 11x + 11h - 4

Step 2: . f(x+h) - f(x) . = . (11x + 11h - 4) - (11x + 4) . = . 11h

. . . . . . . .f(x+h) - f(x) . . . 11h
Step 3: . -------------- . = . ----- . = . 11 . . . . there!
. . . . . . . . . . . h . . . . . . . . .h

 

[witlesswiz]

I appreciate the help, especially the step by step. I am going to have to "meditate" on this for awhile...