WEEK 4 GENMATH

WEEK 4 GENMATH

Inverse Functions

Multiple Choice

K = {(1, 2), (2, 4), (3, 6), (4, 8)} is a ONE-to-ONE function.

• TRUE

• FALSE

Multiple Choice

The relation pairing a studnt to his or her LRN

is a ONE-to-ONE function.

• TRUE

• FALSE

Multiple Choice

The relation pairing a real number to its cube

is a ONE-to-ONE function.

• TRUE

• FALSE

One-to-one Functions

It is a function in which every element in the range of a function corresponds to exactly one element in the domain.

Multiple Choice

Find the inverse function of

K = {(1, 2), (2, 4), (3, 6), (4, 8)}.

• $$K^{-1}=(2,1),(2,4),(6,3),(4,8)$$  

• $$K^{-1}=(2,1),(4,2),(6,3),(8,4)$$  

• $$K^{-1}=\left\{(-1,-2),(-2,-4),(-3,-6),(-4,-8)\right\}$$  

Multiple Choice

Find the inverse of f(x) = 3x + 6.

• $$f^{-1}\left(x\right)=\frac{𝒙−𝟔}{3}$$  

• $$f^{-1}\left(x\right)=3x-6$$  

• $$f^{-1}\left(x\right)=\frac{x+6}{3}$$  

Finding Inverse Functions

For functions expressed as f(x),

1. Replace f(x) with y.

2. Interchange x and y.

3. Solve for the new y.

4. Replace the new y with f^-1(x).

Multiple Choice

Find the inverse of $$g\left(x\right)=\frac{x-5}{4}$$  .

• $$g^{-1}\left(x\right)=\frac{4}{x-5}$$  

• $$g^{-1}\left(x\right)=4x-5$$  

• $$g^{-1}\left(x\right)=4x+5$$  

Multiple Choice

Find the inverse of $$h\left(x\right)=x^3$$  .

• $$h^{-1}\left(x\right)=-x^3$$  

• $$h^{-1}\left(x\right)=\sqrt[3]{x}$$  

• $$h^{-1}\left(x\right)=x^{-3}$$  

Multiple Choice

Find the inverse of 4y – 7x = 5

• $$f^{-1}\left(x\right)=4x+\frac{5}{7}$$  

• $$f^{-1}\left(x\right)=\frac{4x-5}{7}$$  

• $$f^{-1}\left(x\right)=\frac{4x+5}{7}$$