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y=chx=(e^x+e^(-x))/2 is decreasing in the interval (- infinity,0) and increasing in (0, infinity)

i know that a function is increasing in (a,b) if for two variables from that interval let's say x' and x" that are related x'<x" than f(x')<f(x"), sot at this case f is increasing in (a,b).

if x'<x", but f(x')>f(x"), than f is decreasing in (a,b).

here is what i did with chx:

x'<x", x',x">0 , then from the monototy of exponential functions we know that e^x'<e^x" and ( 1/e^x")<(1/e^x')..

here is where i get stuck..

any help????