INVERSE FUNCTIONS.

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Presentation transcript:

INVERSE FUNCTIONS

Steps for Finding the Inverse of a Function y = f -1(x) Solve for y Trade x and y places Replace f(x) with y

Let’s check this by doing Find the inverse of y = f -1(x) Solve for y Trade x and y places Replace f(x) with y

Find the inverse of a function : Example 1: f(x) = 6x - 12 Step 1: Change f(x) to y: y = 6x - 12 Step 2: Switch x and y: x = 6y - 12 Step 3: Solve for y: x +12 = 6y 𝒙+𝟏𝟐 𝟔 =y 𝒚= 𝒙 𝟔 +2 Step 4: Change y to 𝒇 −𝟏 𝒙 : 𝒇 −𝟏 (x) = 𝒙 𝟔 +2

Given the function: f(x) = 3x2 + 2 find the inverse: Example 2: Given the function: f(x) = 3x2 + 2 find the inverse: Step 1: Change f(x) to y: y = 3x2 + 2 Step 2: Switch x and y: x = 3y2 + 2 Step 3: Solve for y: Step 4: Change y to 𝒇 −𝟏 𝒙 : 𝑓 −1 (𝑥)= 𝑥−2 3

Ex: Find an inverse of y = -3x+6. Steps: -switch x & y -solve for y y = -3x+6 x = -3y+6 x-6 = -3y

Finding the Inverse Try