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Brian McLogan
4g Warm up (Graphs of Inverse Trig Functions)
4g Warm up (Graphs of Inverse Trig Functions)
Khan Academy
Khan Academy: Linear Algebra: Introduction to the Inverse of a Function
Video first reviews what a function is. Explains what the identity function is and uses it to define what makes a function invertible. Shows that the inverse will be unique. This video also appears in the strand Algebra: Functions. [18:53]
Khan Academy
Khan Academy: Linear Algebra: Determining Whether a Transformation Is Onto
Video reviews from previous videos that a function is invertible if and only if it is onto and one-to-one. Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the...
Khan Academy
Khan Academy: Linear Algebra: Relating Invertibility to Onto and One to One
Video first reviews that a function is invertible if and only if there is a unique solution to f(x) = y for any y. Extends this to show that a function is invertible if and only if it is surjective (onto) and injective (one-to-one). [6:31]
Khan Academy
Khan Academy: Linear Algebra: Invertibility Implies a Unique Solution to F(x)=y
Video first reviews what it means for a function to be invertible. Shows that if a function is invertible then there is a unique solution to f(x) = y. Also shows that if there is a unique solution to the equation f(x) = y for all y then...