Finding Inverses and Absolute Values

An inverse function reverses the operation of the original function. If the function f takes an input x to produce an output y, then the inverse function f⁻¹ takes y back to x.

To find the inverse of a function, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

To solve an equation with absolute values, set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

To solve a quadratic equation by finding square roots, isolate the x² term and take the square root of both sides, remembering to consider both the positive and negative roots.