(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a, b and c are nonzero distinct real numbers and c > 0. The even function given by:

f(x) = (ax + b)/(x + c)

is constant for -c < x < c and it's value is

(i) a + b; (ii) a + c; (iii) c; (iv) b; (v) a

2. Relevant equations

3. The attempt at a solution

Okay, so first I solved for x but got two different answers because the function is even:

x = (b - f(x)c)/(f(x) - a) and x = (b - f(x)c)/(a - f(x))

Then I wanted to check the conditions on f(x) for -c < x < c:

-c < (b - f(x)c)/(f(x) - a)

But I don't know how to proceed, because I want to divide both sides by (f(x) - a) and I don't know if it's a negative number or not. What should I do here? How does the information given in the problem statement help me at this point? Am I taking a wrong approach at this problem?

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# Homework Help: Conditions for a function to be constant

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