Question

Determine if the inverses listed for each function are correct or not. Select Correct or Incorrect for each function and inverse.

Function and Inverse
Correct
Incorrect
Rx) = 3x
O
Rx) = 3x + 7
F(x) = x - 3
VX-6
x =
O
O

Answer 1

Explanation:

1). f(x) = 3x⁵

Step - 1

Convert the given function in the form of an equation.

y = 3x⁵

Step - 2

Interchange x by y.

Step - 3

Solve the equation for y

x = 3y⁵

y⁵ =
`(x)/(3)`

`y=\sqrt[5]{(x)/(3)}`

Step - 4

Convert the equation into function.

`f^(-1)(x)=\sqrt[5]{(x)/(3)}`

Correct.

2). f(x) = 3x + 7

Step - 1

y = 3x + 7

Step - 2

x = 3y + 7

Step - 3

3y = x - 7

y =
`(1)/(3)(x-7)`

Step - 4

`f^(-1)(x)=(1)/(3)(x-7)`

Correct.

3). f(x) = 6 + 4x³

Step - 1

y = 4x³ + 6

Step - 2

x = 4y³ + 6

Step - 3

y =
`\sqrt[3]{(1)/(4)(x-6)}`

Step - 4

`f^(-1)(x)=\sqrt[3]{(1)/(4)(x-6)}`

Incorrect.