f(x)=sqrt(x)
f'(x)=1/(2sqrt(x))
The function f(x) = √x is a typical example of a square root function. It is defined for all non-negative real numbers. Here are some details about the function:
1. Domain: The domain of the function is [0, +∞). This means that the function is defined for all non-negative real numbers.
2. Range: The range of the function is [0, +∞). This means that the function can take any non-negative real number as its output.
3. Odd function: The square root function is an odd function, which means that f(-x) = -f(x) for all values of x in the domain.
4. Graph: The graph of the square root function is a curve that starts at the point (0, 0) and increases without bound. The curve is continuous and smooth.
5. Properties:
– The function is monotonically increasing, which means that as x increases, f(x) also increases.
– The function is continuous and differentiable for all x > 0.
– The function has a horizontal asymptote of y = 0 as x approaches negative infinity.
– The function has a vertical asymptote of x = 0 as y approaches positive infinity.
– The function is not defined for negative values of x.
In summary, the square root function is an important function in mathematics, and it has many interesting properties and applications.
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