Function Inverse Quick review. {(2, 3), (5, 0), (-2, 4), (3, 3)} Domain & Range = ? Inverse = ? D = {2, 5, -2, 3} R = {3, 0, 4}

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Presentation transcript:

Function Inverse Quick review. {(2, 3), (5, 0), (-2, 4), (3, 3)} Domain & Range = ? Inverse = ? D = {2, 5, -2, 3} R = {3, 0, 4}

Function Inverse {(2, 3), (5, 0), (-2, 4), (3, 3)} Inverse = switch the x and y, (domain and range) I = {(3, 2), (0, 5), (4, -2), (3, 3)}

Function Inverse {(4, 7), (1, 4), (9, 11), (-2, -1)} Inverse = ? I = {(7, 4), (4, 1), (11, 9), (-1, -2)}

Function Inverse Now that we can find the inverse of a relation, let’s talk about finding the inverse of a function. What is a function? a relation in which no member of the domain is repeated.

Function Inverse To find the inverse of a function we will still switch the domain and range, but there is a little twist … We will be working with the equation.

Function Inverse So what letter represents the domain? x So what letter represents the range? y

Function Inverse So we will switch the x and y in the equation and then resolve it for … y.

Function Inverse Find the inverse of the function f(x) = x + 5. Substitute y for f(x). y = x + 5. Switch x and y. x = y + 5 Solve for y. x - 5 = y

Function Inverse So the inverse of f(x) = x + 5 is y = x - 5 or f(x) = x - 5.

Function Inverse Given f(x) = 3x - 4, find its inverse (f -1 (x)). y = 3x - 4 switch. x = 3y - 4 solve for y. x + 4 = 3y y = (x + 4)/3

Function Inverse Given h(x) = -3x + 9, find it’s inverse. y = -3x + 9 x = -3y + 9 x - 9 = -3y (x - 9) / -3 = y

Function Inverse Given Find the inverse.

Function Inverse

Function Inverse 3x = 2y + 5 3x - 5 = 2y

Function Inverse Given f(x) = x y = x x = y x + 4 = y 2

Function Inverse x + 4 = y 2