Answer:
Explanation:
To determine the domain of a function, we need to find the values of x for which the function is defined. In this case, we have three functions: f(x) = x^1, g(x) = 3e^x, and h(x) = 1/√(x - 1). Let's find the domain of each function step by step:
A) For the function f(x) = x^1:
The function f(x) is a simple polynomial function. Polynomial functions are defined for all real numbers. So, the domain of f(x) is all real numbers, which can be expressed as (-∞, ∞).
Now, let's move on to the other functions:
B) For the function g(x) = 3e^x:
The function g(x) is an exponential function, and exponential functions are defined for all real numbers. Therefore, the domain of g(x) is also (-∞, ∞).
C) For the function h(x) = 1/√(x - 1):
In this case, we have a square root function in the denominator. To ensure that the function is defined, the expression inside the square root must be greater than zero, and the denominator must not be equal to zero. So, we have:
x - 1 > 0 (for the square root to be defined)
x > 1
Also, x - 1 ≠ 0 (for the denominator not to be zero)
x ≠ 1
Therefore, the domain of h(x) is (1, ∞), excluding x = 1.
In summary:
A) The domain of f(x) is (-∞, ∞).
B) The domain of g(x) is (-∞, ∞).
C) The domain of h(x) is (1, ∞) excluding x = 1.