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Marina86 [1]
2 years ago
10

The functions $f$ and $g$ are defined as follows: \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}

{\sqrt{x-1}}.\]Explain why the functions $f$ and $g$ are not the same function. Please help, I can’t seem to find the domain of f :(
Mathematics
1 answer:
CaHeK987 [17]2 years ago
5 0

Answer:

The answer is "domain and range are different".

Step-by-step explanation:

Given:

f(x) = \sqrt{\frac{x+1}{x-1}}\\\\g(x) =\frac{\sqrt{x+1}}{\sqrt{x-1}}\\

Solve f(x) to find domain and range:

for element x: R:

⇒ x \leq -1 \ \ \ and \  \ \  x > 1 range:

for  \ \ f(x) \times element : 0 \leq f(x)< 1 \ \ \ or \ \ f(x)>1

g(x) =\frac{\sqrt{x+1}}{\sqrt{x-1}}\\

Solve for domain:

⇒ \ when \ x \ element \ R: \ \ \ x>1  

Solve for range:  

⇒ g(x) \times element  R : g(x)>1

So, the value of the method f(x) and g(x) (range and domain) were different.  

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