Question

Simplify f(1+h)-f(1)/h for f(x)=1/x

Answer 1

lets take it step by step

Answer 2

Ok thank you.

Answer 3

\[f(1)=\frac{1}{1}=1\]\[f(1+h)=\frac{1}{1+h}\]
\[f(1+h)-f(1)=\frac{1}{1+h}-1\]
now some algebra

Answer 4

It's showing something about a math processing error and will not allow me to view your response.

Answer 5

\[\frac{1}{1+h}-1=\frac{1}{1+h}-\frac{1+h}{1+h}=\frac{1-(1+h)}{1+h}\]

Answer 6

Actually its,

Answer 7

refresh your browser, it should show up

Answer 8

@satellite73

Answer 9

let me know if it shows up

Answer 10

It showed up thank you very much. But i have to find f(x) = 1/x with the equation.

Answer 11

\[\frac{1-1-h}{1+h}=\frac{-h}{1+h}\]so
\[f(1+h)-f(1)=\frac{-h}{1+h}\]

Answer 12

now our last job is to divide by \(h\) which is easy because they cancel, and you get
\[\frac{f(1+h)-f(1)}{h}=\frac{-1}{1+h}\]

Answer 13

@MacyK2011 you do not "find \(f(x)=\frac{1}{x}\) you are given that \(f(x)=\frac{1}{x}\) and you are asked for the "difference quotient"
\[\frac{f(1+h)-f(1)}{h}\]

Answer 14

Oh. So what good is the f(x)=1/x? lol

Answer 15

Could you elaborate on difference quotients? Sorry I do not understand them well.

Answer 16

\(f\) is a function, in this case you have \(f(x)=\frac{1}{x}\) a specific function
general difference quotient is for a general function \(f\) is
\[\frac{f(x+h)-f(x)}{h}\]