Question
Give the domain and range of the functions
h(x) = f(x)/g(x), if f(x) = Square root of x-2
and
g(x) is not equal to zero
h(x) = f(x)/g(x), if f(x) = Square root of x-2
and
g(x) is not equal to zero
Answers
GPT 3.5
The domain of h(x) is the set of all real numbers except for x = 2 (since the square root of a negative number is undefined).
For the range, we first need to determine the range of f(x) and g(x). Since f(x) = √(x-2) will always be positive or zero, the range of f(x) is [0, ∞).
Since g(x) is not equal to zero, it can take on any positive or negative value, except zero. Therefore, the range of g(x) is (-∞, 0) ∪ (0,∞).
When we divide f(x) by g(x), the range of h(x) will be all real numbers except when g(x) is equal to zero. Therefore, the range of h(x) is (-∞, 0) ∪ (0, ∞).
For the range, we first need to determine the range of f(x) and g(x). Since f(x) = √(x-2) will always be positive or zero, the range of f(x) is [0, ∞).
Since g(x) is not equal to zero, it can take on any positive or negative value, except zero. Therefore, the range of g(x) is (-∞, 0) ∪ (0,∞).
When we divide f(x) by g(x), the range of h(x) will be all real numbers except when g(x) is equal to zero. Therefore, the range of h(x) is (-∞, 0) ∪ (0, ∞).