josephraven7942
12.07.2019 •
Mathematics
If f(x)=square root of 2-x and g(x)=x-1, then find the domain of h(x)=f(x)/g(x)
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Ответ:
, we know that the function will be undefined when 2 - x < 0, or when x > 2, so we have the restriction on our domain that x ≥ 0.
g(x) has no such restrictions and is defined for all possible values of x, so its domain is all real numbers, or .
Since h(x) is a rational function, we know that it's undefined when its denominator is 0. In this case, our denominator is g(x), so the function is undefined when g(x)=0. x - 1 = 0 only when x = 1, so the second restriction on our domain for h is that x ≠ 1. Putting those two together, we find that the domain of h(x) is all values of x ≥ 0, where x ≠ 1.
Ответ:
Domain of h(x) : [2,∞)
Step-by-step explanation:
Given: Two functions
Composite function,
, It is square root function. As we know square root function is always greater than 0.
2-x ≥ 0
2 ≥ x
Domain of f(x) : [2,∞)
, It is straight line equation (Linear function) As we know domain of linear function is all real number.
Domain of g(x) : (-∞,∞)
, It is rational function. Denominator can't be zero.
So, x-1 ≠ 0
x ≠ 1
Now, we will see domain of h(x) common all three domain.
Domain of h(x): [2,∞)
Hence, The domain of h(x) is [2,∞)
Ответ:
they can be chosen 10 ways since 6 + 4 = 10
Step-by-step explanation: