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SWBAT: Find the Inverse of a Function
SWBAT: Find the Inverse of a Function
2 g
3(2)-2 4
h
-4(4)-2 -18
6 g
(6)2+3 39
h
3(39)+3 120
Page 45
SWBAT: Find the Inverse of a Function
f-1 means inverse
SWBAT: Find the Inverse of a Function
𝒇−𝟏 𝒙 = 𝟕, 𝟑 , 𝟏, 𝟓 , 𝟏, 𝟕
𝑻𝒉𝒆 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏 𝒘𝒂𝒔 𝒏𝒐𝒕 𝟏 − 𝟏, 𝒔𝒐 𝒕𝒉𝒆 𝒊𝒏𝒗𝒆𝒓𝒔𝒆 𝒊𝒔 𝒏𝒐𝒕 𝒂 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏.
SWBAT: Find the Inverse of a Function
Switch “x” and “y”
f(x) = 2x + 4
f-1(x) = ½x -2
SWBAT: Find the Inverse of a Function
𝒚 = 𝟐𝒙 + 𝟑
Switch “x” and “y”
𝒙 = 𝟐𝒚 + 𝟑
Solve for “y”
𝒙 − 𝟑 = 𝟐𝒚 𝒙−𝟑
𝟐= 𝒚 = 𝒇−𝟏(𝒙)
SWBAT: Find the Inverse of a Function
𝒚 = 2
3𝒙 + 𝟒
𝒙 = 2
3𝒚 + 𝟒
𝒙 − 𝟒 = 2
3𝒚 𝟑 ∙ ∙ 3
𝟑𝒙 − 𝟏𝟐 = 2𝑦
𝟑𝒙−𝟏𝟐
𝟐= 𝒚 = 𝒇−𝟏(𝒙)
SWBAT: Find the Inverse of a Function
𝒙 = 𝟐𝒚 − 𝟏3
𝑥 = 𝟐𝒚 − 𝟏3 3
𝑥3 = 2𝑦 − 1
𝑥3 + 1 = 2𝑦
𝒙𝟑+𝟏
𝟐= 𝒚 = 𝒇−𝟏(𝒙)
𝒙 = 𝟐𝒚𝟐 − 𝟏
𝒙 + 𝟏 = 𝟐𝒚𝟐
𝒙 + 𝟏
𝟐= 𝒚𝟐
𝒙+𝟏
𝟐 = 𝑦2
𝒙+𝟏
𝟐 =
2𝑥+2
2 = 𝒚 = 𝒇−𝟏(𝒙)
SWBAT: Find the Inverse of a Function
SWBAT: Find the Inverse of a Function
SWBAT: Find the Inverse of a Function
SWBAT: Find the Inverse of a Function
SWBAT: Find the Inverse of a Function
SWBAT: Find the Inverse of a Function