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Andreyy89
3 years ago
10

evaluate the difference quotient for the given function. Simplify your answer. f(x)=1/x , (f(x) - f(a))/x-a

Mathematics
2 answers:
sergij07 [2.7K]3 years ago
6 0
Fx - a f - a x/ x
That's what I came up with
Bess [88]3 years ago
3 0

The formula for difference quotient is \frac{f(x)-f(a)}{x-a}

Here f(x) = \frac{1}{x}

So f(a) = \frac{1}{a}

First we shall find f(x) - f(a)

We get

f(x) - f(a)

==\frac{1}{x}-\frac{1}{a}

Making denominators same we get

\frac{a}{ax}-\frac{x}{ax}

So we get

f(x) - f(a) = \frac{a-x}{ax}

So the difference quotient shall be

\frac{f(x)-f(a)}{(x-a)}=\frac{\frac{a-x}{ax}}{(x-a)} =\frac{a-x}{ax(x-a)}

Hence the difference quotient is

\frac{f(x)-f(a)}{(x-a)}=\frac{a-x}{ax(x-a)}

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