Question

Anmol says f(x) = x + 1 / x^2 − 1 and g(x) = 1 / x − 1 represent the same function. Is she correct? Justify your answer.

Answer 1

Answer:

No, she is not correct because the functions have different domains.

Step-by-step explanation:

Hi there!

No, she is not correct. Let´s find the values of x for which each function is defined. Any value of x that makes the denominator to be zero, will not be included in the domain of the function:

For f(x):

x² - 1 = 0

Add 1 to both sides of the equation:

x² = 1

Apply the square root to both sides of the equation:

√x² = √1

x = 1 and x = -1

For g(x):

x-1 = 0

add 1 to both sides of the equation:

x = 1

Then, g(x) is defined for all real numbers except 1 while f(x) is defined for all real numbers except 1 and -1. The functions have different domains and, therefore, are no the same.

Have a nice day!