If is the inverse function of , then the domain of is the range of and the range of is the domain of . Like the variables and are 'flipped' to find the inverse function, the domain and range are also 'flipped'.
The graph of crosses the x-axis if and only if . However, never equals 0 because the discriminant of is negative. To review, the discriminant of is given by .
You may recall the discriminant reveals the number of real solutions to a quadratic equation. If the disciminant is positive, there are 2 real solutions and the graph crosses the x-axis twice. If the discriminant is zero, there is one real solution and the graph crosses the x-axis once. If the discriminant is negative, there are no real solutions and the graph does not cross the x-axis.
Before you can find the discriminant of , you have to expand . For example, .
To find the x-intercept(s) of , substitute and solve for .
Multiply both sides of the equation by .
Anything times 0 is still 0.
Distribute into .
and cancel, producing 1.
Subtract 1 from both sides of the equation.
Divide by 2 on both sides of the equation.
Add 1 to both sides of the equation.
Find the least common denominator of and .
Write the left side of the equation as only one fraction.
Simplify the numerator.