Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad \text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]ex plain 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.

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step-by-step explanation:

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the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.