Inverse Functions

F(x) = x + 11

Then use 4 step to find inverse F^-1(x)

• S1: let F(x) = x + 11

  S2: Interchange x <=> y

  x = y + 11

  S3: Solve for y

  11x = y

  S4: F(x)^-1 = 11x

• S1: let y = x + 11

  S2: Interchange x <=> y

  y + 11 = x

  S3: Solve for y

  y = x + 11

  S4: F(x)^-1 = x + 11

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = y + 11

  S3: Solve for y

  x - 11 = y

  S4: F(x) = x

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = y + 11

  S3: Solve for y

  x - 11 = y

  S4: F^-1(x) = x - 11

Tags

CCSS.HSF.BF.B.4

F(x) = 11x

Then use 4 step to find inverse F^-1(x)

• S1: let F(x), x = 11y

  S2: Interchange x <=> y

  y = 11x

  S3: Solve for y

  y = x

  S4: F(x)^-1 = x

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = 11y

  S3: Solve for y

  y = 11x

  S4: F(x)^-1 = 11x

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = 11y

  S3: Solve for y

  x/11 = y

  S4: F(x)^-1 = x/11

• S1: let y = x + 11

  S2: Interchange x <=> y

  x = 11y

  S3: Solve for y

  11/x = y

  S4: F(x) = 11/x

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

G(x) = x/11 . Find G^-1(x)

• S1: Let G(x) = y = x/11

  S2: x <=> y

  x = y/11

  S3: solve for y

  11x = y

  S4: y = G(x)^-1 = 11x

• S1: Let G(x) = y = 11/x

  S2: x <=> y

  x = 11/y

  S3: solve for y

  11/x = y

  S4: y = G(x)^-1 = 11/y

• S1: Let G(x) = y = x/11

  S2: x <=> y

  x = 11y

  S3: solve for y

  x/11 = y

  S4: y = G(x)^-1 = x/11

• S1: Let G(x) = y = x/11

  S2: x <=> y

  x = y/11

  S3: solve for y

  x - 11 = y

  S4: y = G(x)^-1 = x - 11

Tags

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

G(x) = x³ . Find G^-1(x)

• S1: Let y = x³

  S2: x <=> y

  x = y3

  S3: solve for y

  x3= y

  S4: G(x)^-1 = 3x

• S1: Let y = x³

  S2: x <=> y

  x = y³

  S3: solve for y

  x/3  = y

  S4: G(x)^-1 = x/3

• S1: Let y = x³

  S2: x <=> y

  x = y³

  S3: solve for y

  x³ = y

  S4: G(x)^-1 = x³

Tags

CCSS.HSF.BF.B.4

Tags

CCSS.HSA.REI.A.2

CCSS.HSF.BF.B.4

G(x) = 4x³ - 1. Find G^-1(x)

• S1: Let

  y = 4x³ - 1

  S2: x <=> y

  x = 4y³ - 1

  S3: solve for y

  (x³  - 1)/4= y

  S4: G(x)^-1 = (x³  - 1)/4

• S1: Let

  y = 4x³ - 1

  S2: x <=> y

  x = 4y³ - 1

  S3: solve for y

  4x³ + 1 = y

  S4: G(x)^-1 = 4x³ + 1

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

Tags

CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.2

CCSS.HSF.BF.B.4

F(x) = 11x - 1

Then use 4 step to find inverse F^-1(x)

• S1: let F(x), x = 11y + 1

  S2: Interchange x <=> y

  y = 11x

  S3: Solve for y

  y = 11/x - 1

  S4: F(x)^-1 = 11/x - 1

• S1: let y = 11x - 1

  S2: Interchange x <=> y

  x = 11y - 1

  S3: Solve for y

  y = 11x + 1

  S4: F(x)^-1 = 11x + 1

• S1: let y = 11x- 1

  S2: Interchange x <=> y

  x = 11y - 1

  S3: Solve for y

  (x + 1)/11 = y

  S4: F(x)^-1 = (x + 1)/11

• S1: let y = 11x - 1

  S2: Interchange x <=> y

  x = 11y + 1

  S3: Solve for y

  x/11 + 1 = y

  S4: F(x) = x/11 + 11

Tags

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

G(x) = (x² + 1)/11 . Find G^-1(x)

• S1: Let

  y = (x² + 1)/11

  S2: x <=> y

  x = (y² + 1)/11

  S3: solve for y

  11x - 1 = y

  S4: G(x)^-1 = 11x - 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

CCSS.HSF.BF.B.4

G(x) = (4x³ - 1)/2. Find G^-1(x)

• S1: Let

  y = (4x³ - 1)/2

  S2: x <=> y

  x = (4y³ - 1)/2

  S3: solve for y

  (2x + 1)/4= y

  S4: G(x)^-1 = (2x + 1)/4

• S1: Let

  y = (4x³ - 1)/2

  S2: x <=> y

  x = (4y³ - 1)/2 

  S3: solve for y

  (2x + 1)³/4  = y

  S4: G(x)^-1 = (2x + 1)³/4

• S1: Let

  y = (4x³ - 1)/2

  S2: x <=> y

  x = (4y³ - 1)/2

  S3: solve for y

  (2x³ + 1)/4= y

  S4: G(x)^-1 = (2x³ + 1)/4

Tags

CCSS.HSA.CED.A.4

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.4