Akash H.

asked • 12/26/17

Find all functions g : R → R such that for any real numbers x and y g(x + y) + g(x)g(y) = g(xy) + g(x) + g(y).

Find all functions g : R → R such that for any real numbers x and y g(x + y) + g(x)g(y) = g(xy) + g(x) + g(y).

1 Expert Answer

By:

Bobosharif S. answered • 12/26/17

Tutor
4.4 (32)

Mathematics/Statistics Tutor

See tutors like this
See tutors like this
This is a linear function, namely g(x)=x.
There is no other functions, satisfying the given functional equation.
 
 
Upvote • 0 Downvote
More
Report

Akash H.

How did you get the solution?
Report

12/27/17

Bobosharif S.

To solve similar functional equations you get and idea (guess which function(s)) should satisfy this equation. I just tried a ax+b and find out that if a=1 and b=0 then it satisfies the equation.
Report

12/27/17

Akash H.

Can you do me a favour by solving two problems below:
1.How many pairs of natural number can be formed whose LCM will be 7000?
2.Let ΔABC be an isosceles triangle with AB = AC. Suppose that the bisector of ∠B meets AC at D and that BC = BD + AD. Determine ∠A.
 
Report

12/27/17

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.