I have got a problem like this :

Let f : R -> R be a function such that there exists constants b, m > 0 and c belongs to R such that

f(x) > mx + c for all x > b

using only the definition of the limit we have to prove that limit of f(x) when x goes to inifinity = inifinity

I have tried to prove it like this :

For all N > 0 if we can find some 'a' > 0 such that x > a implies (mx + c) > N

then that in turn implies f(x) > N

So that we can say limit of f(x) when x goes to inifinity = inifinity

But the problem is I can't find an 'a' > 0 for this.

I have tried to write it in reverse to find an 'a'

i.e mx + c > N

x > (N-c)/m

But here I get stuck coz 'c' can be either >= N or <N

So, can somebody please help me with this ?

What I need to do is a rigorous proof.