Determine the range and function defined as y=sqrt (25-x^2)
y=
for domain
25-x^2>=0
x^2<=25
therefor x belongs to [-5,5]
hence domain is [-5,5].
Since its minimum value is 0 and maximum 5 and the function is continuous in its domain so its range is [0,5]
note:I hope you know what is range and what is domain.if you have a doubt,you may ask it.
The Domain of a given function is the set of 'input' values (In this case , the values) for which the function is defined.
The function, , is a composed square root function. The domain is found by solving the inequality .
Therefore the domain will be .
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The Range of a given function is the set of 'output' values (In this case , the values) for the function.
The function, , is a quadratic hence values will give the same range. (This is a many to one function)
When . When .
Therefore the range is
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Visually, when a graph is drawn, the domain and range can be seen.