Square Root Functions - Key Features, Transformations, Inverses

A square root function is a function of the form f(x) = $$\frac{{\text{a}}}{{\text{b}}}$$ , where a and b are constants. It represents the principal square root of x.

The domain of the square root function is [0, ∞) because the square root of a negative number is not defined in the set of real numbers.

The range of the square root function is [0, ∞) because the output of the square root function is always non-negative.

To find the inverse of a function, swap the x and y variables and solve for y.

The inverse function f^-1(x) is found by solving the equation x = $$\frac{{\text{a}}}{{\text{b}}}$$ for y.

A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once.

The transformed function is f(x) = $$\frac{{\text{a}}}{{\text{b}}} - 4$$ .

The graph of a function and its inverse are reflections of each other over the line y = x.

If (a, b) is a point on the function f(x), then (b, a) will be a point on the inverse function f^-1(x).

The inverse function is y = $$\frac{{\text{b}}}{{\text{a}}}$$ .