Inverse Functions Pre Calculus 1 6 Inverse Functions

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Inverse Functions Pre. Calculus 1 -6

Inverse Functions Pre. Calculus 1 -6

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Is this function one-to-one? No Inverse Functions

Is this function one-to-one? No Inverse Functions

 • Two functions are inverse functions, when the combination of those functions, in

• Two functions are inverse functions, when the combination of those functions, in any order results, in the identity function. • If the function is given as a set of ordered pairs, its inverse would have all the xcoordinates interchanged with their corresponding y-coordinates. Inverse Functions

Inverse Functions

Inverse Functions

 • The functions f and g are inverses of each other if and

• The functions f and g are inverses of each other if and only if – f(g(x)) = x for every x in the domain of g, and – g(f(x)) = x for every x in the domain of f. – In this case we write g as f-1 Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Find the inverse of the function Inverse Functions

Find the inverse of the function Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Exploration

Exploration

One-to-one function Not one-to-one Not a function One-to-one function Chairs are assigned to people

One-to-one function Not one-to-one Not a function One-to-one function Chairs are assigned to people # of molecules assigned to student Spleens are assigned to people Not a function, could have more than one pencil One-to-one function Not one-to-one function One-to-one function? ? ? SSN are assigned to people Days are assigned to people Not a function Not one-to-one? ? Exploration Not a function One-to-one function Same as function

 • Inverse Functions • pg. 69 – 70 • 11 a, 21 -24,

• Inverse Functions • pg. 69 – 70 • 11 a, 21 -24, 31, 32, 45, 47, 48, 50, 63, 67 Homework