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We know that in order to find the inverse of a function algebraically, we need to swap x and y and then solve for y. In doing this, the domain and range get swapped, as well. We can see this graphically as a function and its inverse are reflected across the line y = x. When working with radical functions in particular, we need to make sure that whatever is under the radical, called the radicand, is always greater than or equal to zero. This will help us verify that the domain and range have been swapped.
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Sample Problems (10)
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Finding an Inverse Algebraically
Problem 1 5,452 viewsFind f⁻¹(x) given
f(x) = (x − 2)³ 
Finding an Inverse Algebraically
Problem 2 4,244 viewsFind g⁻¹(x) given
g(x) = x² + 2 
Finding an Inverse Algebraically
Problem 3 340 views 
Finding an Inverse Algebraically
Problem 4 267 views 
Finding an Inverse Algebraically
Problem 5 260 views 
Finding an Inverse Algebraically
Problem 6 248 views 
Finding an Inverse Algebraically
Problem 7 234 views 
Finding an Inverse Algebraically
Problem 8 206 views 
Finding an Inverse Algebraically
Problem 9 275 views 
Finding an Inverse Algebraically
Problem 10 254 views
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