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

let f: R->R be a continuous function

Suppose k>=1 is an integer such that

lim f(x)/x^k = lim f(x)/x^k = 0

x->inf x->-inf

set g(x)= x^k + f(x)

g: R->R

Prove that

(i) if k is odd, then g is surjective

(ii) if k is even, then there is a real number y such that the image of g is [y,inf)

2. Relevant equations

3. The attempt at a solution

I am completely stuck at this all I can think of is x^k goes to infinity then the ratio of the functions can go to 0 if either f(x) goes to 0 or f(x) is a constant or f(x) goes to infinity slower than x^k (I am not sure about this)

Any help will be very much appreciateve

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# Homework Help: Ratio of functions, surjective (analysis course)

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