Prove that if $f(x)=a/(x+b)$ then $f((x_1+x_2)/2)\le(f(x_1)+f(x_2))/2$ This exercise :  

If  $f(x)=a/(x+b)$ then : $$ f((x_1+x_2)/2)\le(f(x_1)+f(x_2))/2$$ 

was in my math olympiad today (for 16 years olds). 
I proved this by saying this is true due to Jensen's inequality.
Is this an acceptable answer?(with leaving aside  the fact that i didn't prove the function is convex since it can't be done with the info we got until now).
Does it have any other way of proving this?

You can prove that f is convex by finding it second derivative, which is positive.
