You are here:

# Algebra/Algebra Problem with Functions

Question
I am really stuck on the following problem.  I just don't know how to set up a path for the solution.  Could you please guide me?

Given that f(x^2 + 1) = 2x + f(x) for all real x and f(0) = 7, find the value of f(5).

I looked at: f(x^2 + 1) = 2x + 7. But that leads me nowhere.  So, I solved x^2 +1 = 2x + 2x +1 for x.  I found that x = 0 and x = 4.  This is where I am stuck.

Thanks,
Jimmy

For  f(x^2 + 1) = 2x + f(x), we shall consider a series of substitutions to help us out.

substituting in x=0, we have

f(1) = 2* 0 +  f(0) = 7

substituting in x=1,

f(1^2 + 1) = f(2) = 2 * 1 + f(1) = 2 + 7 = 9   ( it is known previously that f(1) = 7 )

substituting in x=2,

f(2^2 + 1) = f(5) = 2* 2 + f(2) = 4 + 9         ( it is known previously that f(2) = 9 )

= 13 (shown)

Hope this helps. Peace.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks, it makes sense now!

Algebra

Volunteer

#### Frederick Koh

##### Expertise

I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.

##### Experience

More than 7 years of experience helping out in various homework forums. Latest presence is over at http://www.thestudentroom.co.uk/. You can also visit my main maths website http://www.whitegroupmaths.com where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

Organizations
IEEE(Institute of Electrical and Electronics Engineers )

Education/Credentials
Former straight As A level student from HCJC (aka HCI); scored distinctions in both C and Further Mathematics B Eng (Hons) From The National University Of Singapore (NUS) B Sc (Hons) From University of London External (Grad Route)