Question

Help with math?

Answer 1

\(f(x) = 7 + 4x\) and \(g(x) = \dfrac{1}{2x} \)

then

\(\large \dfrac{f}{g}(x) = \dfrac{7 + 4x}{\frac{1}{2x} }\)

Can you simplify the right side of the expression above?

Answer 2

I'm not really sure how, but I can try.

I think the denominator can be simplified to .5x, no?

Answer 3

Yes, you can do that, but let me show you a different way.

Answer 4

remember that a fraction is really a division, so think of

\(\Large \dfrac{7 + 4x}{\frac{1}{2x}} \)

as

\((7 + 4x) \div \dfrac{1}{2x} \)

How do you divide by a fraction?
(Remember about multiplying by the reciprocal?)

Answer 5

First you multiply the number by the reciprocal of the fraction.
And then you simplify the resulting fraction if you can.
Right?

Answer 6

Correct.
Set up the division as the multiplication by the reciprocal.

\((7 + 4x) \div \dfrac{1}{2x} = (7 + 4x) \times 2x = 2x(7 + 4x)\)

Now can you simplify it by distributing the 2x?

Answer 7

14x + 8x^2?

Answer 8

And then we plug in the 5?

Answer 9

yes

Answer 10

Exactly.
Good job, btw.

Answer 11

Thanks so much!!!

Answer 12

your welcome evern though i helped at the end

Answer 13

To recap:

\(f(x) = 7 + 4x\) and \(g(x) = \dfrac{1}{2x}\)

\(\dfrac{f}{g}(x) = \dfrac{7 + 4x}{\frac{1}{2x}} \)

\(\dfrac{f}{g}(x) = (7 + 4x) \times 2x \)

\(\dfrac{f}{g}(x) = 14x + 8x^2 \)

\(\dfrac{f}{g}(5) = 14(5) + 8(5)^2 \)

\(\dfrac{f}{g}(5) = 70 + 200 \)

\(\dfrac{f}{g}(5) = 270 \)

Answer 14

You're welcome.