Question

The graph of the function f(x)=1/x is shifted and written as g(x)=1/x−12. Which of the following is the correct domain for the function g(x) ?(1 point) Responses
A. (−∞<x<0)∪(0<x<∞)
B. (−∞,12)∪(12,∞)
C. (−∞,−12)∪(−12,∞)
D. {x: x∈r,x≠−12}

Answer 1

To determine the correct domain for the function \( g(x) = \frac{1}{x} - 12 \), we first need to consider the domain of the original function \( f(x) = \frac{1}{x} \).

The function \( f(x) = \frac{1}{x} \) is defined for all real numbers except \( x = 0 \), since division by zero is undefined. Thus, its domain is \( (-\infty, 0) \cup (0, \infty) \).

Now, let's analyze the transformation applied to create \( g(x) \):
- The term \( -12 \) is a constant and does not affect the values of \( x \). The only value of \( x \) that would still make \( g(x) \) undefined is when \( x = 0 \).

So, the domain of \( g(x) = \frac{1}{x} - 12 \) remains the same as that of \( f(x) \):
- The domain of \( g(x) \) is \( (-\infty, 0) \cup (0, \infty) \).

Looking at the answer choices provided:
- **A. \( (-\infty < x < 0) \cup (0 < x < \infty) \)** is the correct notation for the domain since it correctly describes the values where \( g(x) \) is defined.

Thus, the correct answer is **A. \( (-\infty < x < 0) \cup (0 < x < \infty) \)**.