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

Answer:

Step-by-step 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 = $\frac{x}{3}$

$y=\sqrt[5]{\frac{x}{3}}$

Step - 4

Convert the equation into function.

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

Correct.

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

Step - 1

y = 3x + 7

Step - 2

x = 3y + 7

Step - 3

3y = x - 7

y = $\frac{1}{3}(x-7)$

Step - 4

$f^{-1}(x)=\frac{1}{3}(x-7)$

Correct.

3). f(x) = 6 + 4x³

Step - 1

y = 4x³ + 6

Step - 2

x = 4y³ + 6

Step - 3

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

Step - 4

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

Incorrect.