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**HallsofIvy** To determine the domain for a function, f(x), look for values where f **cannot** be applied. Given f(x)= ax^(1/3)+ b, we can take the cube root of any number, we can multiply any number by a and we can add b. The domain is 'all numbers'. To determine the range, **solve** the equation for x. From y= ax^(1/3)+ b, ax^(1/3)= y- b, x^(1/3)= y/a+ b/a, and, finally, x= (y/a+ b/a)^3. For any value of y we can: divide by a, add b/a, and then cube. The range is "all numbers'.

A more interesting function is y= x^2. we can, of course, square any number so the domain is 'all numbers'. But solving for x involves taking the square root of y. We can only take the square root (x and y are real numbers here) of non-negative numbers. The range is 'all non-negative numbers".