Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]explain why f and g are not the same function.

The given functions are not same because the domain of both functions are different.

Step-by-step explanation:

The given functions are

First find the domain of both functions. Radicand can not be negative.

Domain of f(x):

This is possible if both numerator or denominator are either positive or negative.

Case 1: Both numerator or denominator are positive.

So, the function is defined for x≥1.

Case 2: Both numerator or denominator are negative.

So, the function is defined for x≤-1.

From case 1 and 2 the domain of the function f(x) is (-∞,-1]∪[1,∞).

Domain of g(x):

So, the function is defined for x≥1.

So, domain of g(x) is [1,∞).

Therefore, the given functions are not same because the domain of both functions are different.

This is a question of whether 91 is a prime number or not. And it is not so Mrs. Fisher is right, you can arrange them in 7 rows and 19 columns or vice versa. 7 and 13 are factors of 91.