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utkarshakash
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Homework Statement
If f and g are two distinct linear functions defined on R such that they map[-1,1] onto [0,2] and h:R-{-1,0,1}→R defined by h(x)=f(x)/g(x) then show that |h(h(x))+h(h(1/x))|>2
Homework Equations
The Attempt at a Solution
I assume f(x) to be ax+b and g(x) to be lx+m so that h(x) is (ax+b)/(lx+m). From here I can write h(h(x)) and h(h(1/x)) but there is nothing I can see that will help me to prove this inequality. Any ideas?