Question 644387
f(x)=8/x 


f(g(x))=8/(g(x))

 
f(g(x))=8/(8/x) 


f(g(x))=(8/1)/(8/x) 


f(g(x))=(8/1)*(x/8) 


f(g(x))=(8x)/(1*8) 


f(g(x))=(8x)/(8) 


f(g(x))=x


The same works in reverse


g(x)=8/x 


g(f(x))=8/(f(x))

 
g(f(x))=8/(8/x) 


g(f(x))=(8/1)/(8/x) 


g(f(x))=(8/1)*(x/8) 


g(f(x))=(8x)/(1*8) 


g(f(x))=(8x)/(8) 


g(f(x))=x


So these both in conjunction show that f and g are inverses of each other.


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