Solving f(x) Substitution: 1/x +1-(1/x)/h

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Homework Help Overview

The discussion revolves around simplifying the expression (f(h+1) - f(h))/h for the function f(x) = 1/x. Participants are exploring the substitution and simplification process involved in this problem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to substitute the function f(x) into the expression and simplify it. Questions arise regarding the correctness of substitutions and whether the problem is being interpreted correctly.

Discussion Status

The discussion is ongoing, with some participants providing guidance on the correct substitutions and simplifications. There is recognition of potential misunderstandings regarding the variables used in the expressions.

Contextual Notes

Some participants question whether the original problem statement might have been misinterpreted, suggesting alternative forms of the expression to consider.

yoleven
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Homework Statement


f(h+1)-f(h)/h. If f(x)=1/x, simplify.


Homework Equations





The Attempt at a Solution


1/x+1-(1/x)/h

is the answer 1/h? I am not sure if i substituted this correctly or if I solved this right.
I put 1/x in everywhere there was a f(h).
 
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If f(x)=1/x, then f(h+1)=1/(h+1), f(5)=1/5. Etc. x is only a dummy variable.
 
Incorrect.

f(h+1)=1/(h+1)

f(h)=1/h

[f(h+1)-f(h)]/h

[1/(h+1)-1/h]/h

Continue.
 
so it should have been (1/x+1 -1/x)/h
dealing with the numerator first, I bring the terms to a common denominator..
(x-x+1/x^2+x)/h.
i multiply the numerator by 1/h and get..
1/hx^2+hx
is that right?
 
You aren't listening. There are NO x's in (f(h+1)-f(h))/h. Reread the previous posts. By the way, are you sure the problem isn't (f(h+1)-f(1))/h??
 
Last edited:
Okay, I can see that now. Thanks.
 

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