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podryga [215]
3 years ago
8

What is the difference quotient for the function f(x) = 8/ 4x + 1

Mathematics
1 answer:
AleksAgata [21]3 years ago
5 0

Answer:

Last option (counting from the top)

Step-by-step explanation:

For a given function f(x), the difference quotient is:

\frac{f(x + h) - f(x)}{h} = \frac{1}{h}*(f(x + h) - f(x))

In this case, we have:

f(x) = \frac{8}{4x + 1}

Then the difference quotient will be:

\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1})

Now we should get a common denominator.

We can do that by multiplying and dividing each fraction by the denominator of the other fraction, so we will get:

\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1}) = \frac{1}{h}*(\frac{8*(4x + 1)}{(4(x + h) +1 )*(4x + 1)} - \frac{8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)})

Now we can simplify that to get:

\frac{1}{h}*\frac{8*(4x + 1) - 8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)}} =  \frac{1}{h}*\frac{-32h}{(4(x + h) +1 )*(4x + 1)}} = \frac{-32}{(4(x + h) +1 )*(4x + 1)}}

Then the correct option is the last one (counting from the top)

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