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

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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