Question

How to solve x - 9/x using the difference quotient?

a) (f(x + h) - f(x))/h
b) (f(x) - f(x - h))/h
c) (f(x + h) - f(x))/x
d) (f(x) - f(x - h))/x

Answer 1

To solve x - 9/x using the difference quotient, use the formula (f(x) - f(x - h))/h. Simplify the expression and cancel out the h terms.

Step-by-step explanation:

To solve the expression x - 9/x using the difference quotient, we need to use the formula (f(x) - f(x - h))/h. Let's assign f(x) as x and plug it into the formula.

(x - 9/x - (x - h - 9/(x - h))) / h

Simplifying further, we get (h - 9(h - 1)/(x(x - h))) / h

Canceling out the h terms, we are left with -9(x - 1)/(x(x - h))

So, the correct option is d. (f(x) - f(x - h))/x.