Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Find the Function g

Given f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g.

Let me see.

(f/g)(x) = f(x)/g(x).

I think the set up is this:

[(1/x)(x + 1)]/(x^2 - 1)

[(x + 1)/x]/(x^2 - 1)

[(x + 1)/x]/(x - 1)(x +1)

[(x + 1)/x] • 1/(x^2 - 1)

[(x + 1)/x] • 1/(x - 1)(x + 1)

My answer: g(x) = 1/[(x)(x - 1)]

You say?

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 256

Re: Find the Function g

Given f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g.
Let me see.
(f/g)(x) = f(x)/g(x).

Let me see:
(f/g)(x) = f(x) / g(x)
(f/g)(x) * g(x) = f(x)
g(x) = f(x) / (f/g)(x)

g(x) = (1/x) / [(x + 1)/(x^2 - x)]
g(x) = (1/x) * (x^2 - x) / [(x + 1)
...

Last edited by KerimF (2024-03-10 01:25:30)

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find the Function g

It's not working for me. Good way to test some algebra is to substitute numbers and check it.

Say x=5.

f(x) = 1/x = 1/5

f/g = (x+1)/(x^2-x) = 6 / (25-5) = 6/20

If f/g = 6/20 then g/f = 20/6 => g = f x 20/6 = 1/5 x 20/6 = 20/30

By your formula

g(5) = 1/(5 x 4) = 1/20 Not what we should be getting.

I suggest you start with g/f = (x^2-x)/(x+1)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 256

Re: Find the Function g

His wrong line is:
[(1/x)(x + 1)]/(x^2 - 1)

The right one is:
(1/x) / [(x + 1)/(x^2 - x)]

He was just in a hurry
So he skipped:
(f/g)(x) * g(x) = f(x)
g(x) = f(x) / (f/g)(x)

Last edited by KerimF (2024-03-10 01:44:19)

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find the Function g

Thank you both. I will play with this one also at the job on lunch break. I work overnight hours. It's just me and another guard in the building.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find the Function g

His wrong line is:
[(1/x)(x + 1)]/(x^2 - 1)

The right one is:
(1/x) / [(x + 1)/(x^2 - x)]

He was just in a hurry
So he skipped:
(f/g)(x) * g(x) = f(x)
g(x) = f(x) / (f/g)(x)

(1/x) / [(x + 1)/(x^2 - x)]

(1/x) / [(x + 1)/x(x - 1)]

(1/x) ÷ [(x + 1)/x(x - 1)]

(1/x) • [x(x - 1)/(x + 1)]

g(x) = (x - 1)/(x + 1)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find the Function g

That's it.

Check: Put x = 5, g(5) = 4/6 = 20/30  tick.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find the Function g

That's it.

Check: Put x = 5, g(5) = 4/6 = 20/30  tick.

Bob

Cool. I must learn how to upload photo here. I cannot continue with all this typing on my phone.