You are here:

# Algebra/Function Problem

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.  Well, that took me nowhere also.

Thanks,
Jimmy

For x^2 + 1 = 5, x^2 = 4, so x=2.
To find f(5), we get f(5) = 2*2 + f(2).

To find f(5), we need to look at x=1, for x^2 + 1 when x=1.  Note that 1^2 + 1 = 2.
This says that f(2) = 2*1 + f(1) = 2 + f(1).  This says that f(5) = 4 + f(2) = 4 + 2 + f(1).
So, that says that f(5) = 6 + f(1).

For x=0, x^1+1=1, so we have f(1) = 2*1 + f(0) = 2 + f(0).
Putting this into the last equation gives f(5) = 6 + 2 + f(0) = 8 + f(0).

Since we are given f(0) = 7, this says that since f(5) = 8 + f(0),
and f(0) = 7, that f(5) = 8 + 7.  Last I knew, that is the same as f(5) = 15.

Algebra

Volunteer

#### Scott A Wilson

##### Expertise

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

##### Experience

I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Publications
Documents at Boeing in assistance on the manufacturiing floor.

Education/Credentials
MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

Past/Present Clients
Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.