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4 years ago

WILL GIVE BRAINLIEST!

Mathematics

1 answer:

Alchen [17]4 years ago

7 0

Answer:

A.The functions f(x) and g(x) are inverses of each other

B. x∈ (-∞ , 0) ∪ (0 , 2) ∪ (2, +∞)

Step-by-step explanation:

To prove the above, we use the following formula:

f⁻¹( f(x) ) = x

where f⁻¹(x) is inverse function and f(x) is original function

In this case we use f(x) as inverse function and g(x) as original function

Composition of functions is:

f(g(x)) = f((2x+1)/x) = 1/(((2x+1)/x) -2) = 1/((2x+1-2x)/x) = 1/(1/x) = x

We get x finally and prove that these functions are inverses to each other.

B. Composition of the functions are possible under following conditions:

x -2 ≠ 0 and x ≠ 0 namely x ≠ 2 and x ≠ 0

Domain is x∈ (-∞ , 0) ∪ (0 , 2) ∪ (2, +∞)

God with you!!!

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