In order to find the inverse of this function, interchange the x and y-variables.

Subtract three from both sides.

Simplify the equation.

Divide by ten on both sides.

Simplify both sides.

The answer is:

Evaluate first. Substitute the function into .

Distribute the integer through the binomial and simplify the equation.

Multiply this expression with .

The answer is:

For any parabola, the general equation is

, and the x-coordinate of its vertex is given by

.

For the given problem, the x-coordinate is

.

To find the y-coordinate, plug into the original equation:

Therefore the vertex is at .

This is a graph of a circle with radius of 5 and a center of (1,1). The center of the circle is not on the edge of the circle, so that is the correct answer. All other points are exactly 5 units away from the circle's center, making them a part of the circle.

The range is the existing y-values that contains the function.

Notice that this is a parabola that opens downward, and the y-intercept is four.

This means that the highest y-value on this graph is four. The y-values will approach negative infinity as the domain, or x-values, approaches to positive and negative infinity.

The answer is:

For any parabola, the general equation is

, and the x-coordinate of its vertex is given by

.

For the given problem, the x-coordinate is

.

To find the y-coordinate, plug into the original equation:

Therefore the vertex is at .

Substitute the assigned values into the expression.

Simplify the inside parentheses.

The answer is:

All inputs are valid. There is nothing you can put in for x that won't work.

The expression under the square root symbol cannot be negative, so to find the domain, set that expression .

The domain includes all x-values less than or equal to 7, which can be written as .

The equation given represents a circle.

represents the center, and is the radius.

The center is at:

Set up an equation to solve the radius.

The radius is:

The answer is: