Finding and Analyzing Inverse Functions In Exercise 45 56 f

Finding and Analyzing Inverse Functions In Exercise 45 - 56, find the inverse function of f, graph both f and f^-1 on the same set of coordinate axes, describe the relationship between the graphs of f and f^-1, and state the domains and of f and f^-1 f(x) = 2x - 3 f(x) = 3x + 1 f(x) = x^5 - 2 f(x) = x^3 + 1 f(x) = squareroot 4 - x^2, 0 lessthanorequalto x lessthanorequalto 2

Solution

Let f(x) = y (for symplicity)

Then y^2 = 4 - x^2

x^2 = 4 - y^2

x = ± sqrt(4 - y^2)

I\'ve shown that any given x-value will actually correspond to two different y-values, one from the \"plus\" on the square root and the other from the \"minus\"

The Inverse is not a Function