For which pairs of functions is f(g(x))=x?
a) f(x)=x^2 and g(x)=1/x
b) f(x)=2/x and g(x)=2/x
c) f(x)x-2/3 and g(x)=2-3x
d) f(x)1/2x-2 and g(x)=1/2x+2

The correct answer is:

B) f(x)=2/x and g(x)=2/x

Explanation:

To perform this composition of functions, we take the value of g(x) for each choice and substitute it in place of x in f(x).  

For this one, we have f(x) = 2/x and g(x) = 2/x.  This means we replace x in f(x) with 2/x:

f(g(x)) = f(2/x) = 2/(2/x)

This can also be written as:

f(2/x) = 2÷(2/x) = (2/1)÷(2/x)

When dividing fractions, flip the second one and multiply:

f(2/x) = (2/1)×(x/2) = (2*x)/(1*2) = (2x)/2 = x

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step-by-step explanation:

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