Introduction :
In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That’s provides an "output" or "value" for each member of the domain.Interval, also called a range; the range between minimum and maximum e.g. the range on 21 22 23 and 24 is 3.Range, the set of all output values produced by a function. (Source: Wikipedia)
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Example problems for domain and range and math:
Domain and range and math – Example problem: 1
In the function of f that can be expressed as f(x) = -1 / (x + 19). Solve the domain function.
Solution:
To find the domain equate denominator to zero
x + 19 = 0
x = -19
The domain function of f lies in the interval (-infinity, -19) U (-19, +infinity)
Domain and range and math – Example problem: 2
In the function of f that can be expressed as the f(x) = x ^2 + 52. Solve the domain function.
Solution:
The function f(x) = x ^2 + 52 is defined for all real values of x.
In the ‘x’ is the real value and f(x) is the domain function.
Since x ^2 is never negative, x ^2 + 52 is never less than 52
Domain and range and math – Example problem: 3
The function of f that can be expressed as f(t) = (1)/(t + 27). Solve the domain function.
Solution:
The function f(t) = (1)/(t + 27) is not defined for t = -27, as this value requires division by zero.
In all the real numbers that except by -27 and the domain function is f(t).
It has no matter how large or small t it becomes, f(t) will never be equal to zero
Domain and range and math – Example problem: 4
The function of f that can be expressed as f (x) = x 2 + 35. Solve the range function.
Solution:
The range of the function f that is the set of all values of f(x) in the interval (35, +infinity)
Domain and range and math – Example problem: 5
In the function of f that can be expressed as f (x) = x 2 + 39. Solve the range function.
Solution:
The range of function f lies in the interval (39, +infinity)
Practice problems for domain and range and math:
1. The function of f that can be defined as f(x) = `sqrt(-x + 59)` . Solve the domain function.
[Answer: The domain function of f that lies in the interval (-infinity , 59) ]
2. The function of f that can be defined as f(x) = `sqrt( -x + 60) / ((x + 37)(x + 51))` . Solve the domain function.
[Answer: The domain function of f that lies in the interval (-infinity , -51) U (-51 , -37) U (-37, 60 ) ]
3. The function of f that can be defined as f (x) = x 2 + 89. Solve the range function.
[Answer: The range of function f that lies in the interval (89, + infinity)]
In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That’s provides an "output" or "value" for each member of the domain.Interval, also called a range; the range between minimum and maximum e.g. the range on 21 22 23 and 24 is 3.Range, the set of all output values produced by a function. (Source: Wikipedia)
Please express your views of this topic What is a Denominator by commenting on blog.
Example problems for domain and range and math:
Domain and range and math – Example problem: 1
In the function of f that can be expressed as f(x) = -1 / (x + 19). Solve the domain function.
Solution:
To find the domain equate denominator to zero
x + 19 = 0
x = -19
The domain function of f lies in the interval (-infinity, -19) U (-19, +infinity)
Domain and range and math – Example problem: 2
In the function of f that can be expressed as the f(x) = x ^2 + 52. Solve the domain function.
Solution:
The function f(x) = x ^2 + 52 is defined for all real values of x.
In the ‘x’ is the real value and f(x) is the domain function.
Since x ^2 is never negative, x ^2 + 52 is never less than 52
Domain and range and math – Example problem: 3
The function of f that can be expressed as f(t) = (1)/(t + 27). Solve the domain function.
Solution:
The function f(t) = (1)/(t + 27) is not defined for t = -27, as this value requires division by zero.
In all the real numbers that except by -27 and the domain function is f(t).
It has no matter how large or small t it becomes, f(t) will never be equal to zero
Domain and range and math – Example problem: 4
The function of f that can be expressed as f (x) = x 2 + 35. Solve the range function.
Solution:
The range of the function f that is the set of all values of f(x) in the interval (35, +infinity)
Domain and range and math – Example problem: 5
In the function of f that can be expressed as f (x) = x 2 + 39. Solve the range function.
Solution:
The range of function f lies in the interval (39, +infinity)
Practice problems for domain and range and math:
1. The function of f that can be defined as f(x) = `sqrt(-x + 59)` . Solve the domain function.
[Answer: The domain function of f that lies in the interval (-infinity , 59) ]
2. The function of f that can be defined as f(x) = `sqrt( -x + 60) / ((x + 37)(x + 51))` . Solve the domain function.
[Answer: The domain function of f that lies in the interval (-infinity , -51) U (-51 , -37) U (-37, 60 ) ]
3. The function of f that can be defined as f (x) = x 2 + 89. Solve the range function.
[Answer: The range of function f that lies in the interval (89, + infinity)]
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