Answer:
A.The functions f(x) and g(x) are inverses of each other
B. x∈ (-∞ , 0) ∪ (0 , 2) ∪ (2, +∞)
Step-by-step explanation:
A.
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!!!
