Irrational Functions with Higher Indices The square root
function is the inverse of the polynomial y = x2. All of the
polynomials whose equation is y = xn, where n is a positive
integer, have inverses. Take a moment to use your graphing
calculator to look at the graphs of y = x4, y = x6, and y = x8.
Do you see that they are very similar to the graph of y = x2?
They are symmetric to the y-axis, they pass through the origin,
and they never drop below the x-axis. Because they fail the
horizontal-line test for 1-1 functions, you must restrict the
domain to be x > 0 in order to have an inverse function. Take a
look at the graphs of y = x3, y = x5, and y = x7. These graphs
are not symmetric to the y-axis, they pass through the origin,
they do have output values that are negative, and they do pass
the horizontal-line test. These functions do have inverses as
they exist, so the domain does not have to be restricted. The
domain of a radical function is x > 0 when the index is even and
is all real numbers when the inde