Find the Difference Quotient f(x)=1/x

Problem

ƒ(x)=1/x

Solution

1. Identify the formula for the difference quotient, which is defined as (ƒ*(x+h)−ƒ(x))/h for h≠0

2. Substitute the function ƒ(x)=1/x into the formula to set up the expression.

(1/(x+h)−1/x)/h

3. Find a common denominator for the terms in the numerator to combine the fractions.

(x−(x+h))/(x*(x+h))/h

4. Simplify the numerator by distributing the negative sign and subtracting the terms.

(−h)/(x*(x+h))/h

5. Divide by h by multiplying the numerator fraction by the reciprocal of the denominator.

(−h)/(x*(x+h))⋅1/h

6. Cancel the common factor of h from the numerator and denominator.

(−1)/(x*(x+h))

Final Answer

(ƒ*(x+h)−ƒ(x))/h=−1/(x*(x+h))

Want more problems? Check here!