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Determine if `f(x)=1/x,g(x)=1/x` are inverses.Consider the functions f(x)=1/x and...

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Determine if `f(x)=1/x,g(x)=1/x` are inverses.

Consider the functions f(x)=1/x and g(x)=1/x

a) Find f(g(x)) (Give any values of x that need to be excluded from f(g(x))

b) Find g(f(x)) (Also, give any values of x that need to be excluded from g(f(x))

c) Determine whether the functions f and g are inverses of each other.

 

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f and g are inverses if `f(g(x))=g(f(x))=x` for all x in the domain.

(1) `f(g(x))=1/(1/x)=x` for `x!=0`

(2) `g(f(x))=1/(1/x)=x` for `x!=0`

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Since f(g(x))=g(f(x))=x the functions are inverses.

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**Graphically, functions are inverses if they are reflections across the line y=x. The graph of `y=1/x:`

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