Domain problem

[sakailoi1234]

Suppose a function f(x) has domain (−1, 1). Find the domains of the following functions:
A. f(x + 1)
B. f(1/x)
C. f(√x)
D. f((x+1)/(x−1))

 

[Deleted member 4993]

Suppose a function f(x) has domain (−1, 1). Find the domains of the following functions:
A. f(x + 1)
B. f(1/x)
C. f(√x)
D. f((x+1)/(x−1))

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What is the definition of the domain of a function?

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[stapel]

Suppose a function f(x) has domain (−1, 1). Find the domains of the following functions:
A. f(x + 1)
B. f(1/x)
C. f(√x)
D. f((x+1)/(x−1))

You are given that the function is defined on (that is, "has rules that make sense for") the interval between x = -1 and x = +1. This means that the input value, after whatever expression has been evaluated and simplified, has to be between -1 and +1.

Suppose they asked for the domain of f(x - 3). Since the input value has to be between -1 and +1, then x - 3 has to be between -1 and +1. Then -1 < x - 3 < +1. Adding 3 to all three "sides", we get -1 + 3 < x - 3 + 3 < +1 + 3, or 2 < x < 4. If you pick ANY x-value between 2 and 4, you'll get an input value for x - 3 which is between -1 and +1. So the domain of g(x) = f(x - 3) is (2, 4).

Follow the same reasoning with your exercise. If you get stuck, please reply showing your work and reasoning so far. Thank you!