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Homework Statement:

Let function ƒ be f(x)=1/x+sin^2(x) and inff(0,∞)=0.
Prove that every c> 0 has a solution to the equation f(x)=c
Relevant Equations:
 
I'm not sure that inff(0,∞)=0 can help But that was the first section of the question so I thought to point it out anyway.
I'm not sure what I'm supposed to do or what I'm supposed to show.
I was thinking of using the right environment of 0 where f aims for infinity but I don't know how it helps me.
I'm not sure what I'm supposed to do or what I'm supposed to show.
I was thinking of using the right environment of 0 where f aims for infinity but I don't know how it helps me.