Question

25 POINTS PLZ HELP ASAP!!!

Match the functions with their inverse functions.

Answer 1

To calculate the inverse isolate x on one side and switch x with y on both sides

1)
y=(2x-3)/5
5y=2x-3
5y+3=2x
(5y+3)/2=x
-> f(x)=(5x+3)/2

2)
y=(x+8)/2
2y=x+8
2y-8=x
-> f(x)=2x-8

3)
y=(x+2)/7
7y=x+2
7y-2=x
-> f(x)=7x-2

4)
y=(1-2x)/x
y=(1/x)-2
y+2=1/x
x=1/(y+2)
-> f(x)=1/(x+2)

Answer 2

Answer with explanation:

We know that when we are given a inverse function as:
`f^(-1)(x)`

Then we find the function by the method:

Put
`f^(-1)(x)=y`

Then we switch the places of x and y and solve for y.

1)

`f^(-1)(x)=(2x-3)/(5)`

Hence, we find the function as follows:

`(2x-3)/(5)=y`

Then we switch for x and y

`(2y-3)/(5)=x\\\\\\i.e.\\\\2y-3=5x\\\\\\i.e.\\\\\\2y=5x+3\\\\\\i.e.\\\\\\y=(5x+3)/(2)`

Hence, inverse function is:

`f(x)=(5x+3)/(2)`

2)

`f^(-1)(x)=(x+8)/(2)`

Hence, we find the function as follows:

`(x+8)/(2)=y`

Then we switch for x and y

`(y+8)/(2)=x`

`y=2x-8`

Hence, inverse function is:

`f(x)=2x-8`

3)

`f^(-1)(x)=(x+2)/(7)`

Hence, we find the function as follows:

`(x+2)/(7)=y`

Then we switch for x and y

`(y+2)/(7)=x`

`y=7x-2`

Hence, inverse function is:

`f(x)=7x-2`

4)

`f^(-1)(x)=(1-2x)/(x)`

Hence, we find the function as follows:

`(1-2x)/(x)=y`

Then we switch for x and y

`(1-2y)/(y)=x`

i.e.

`1-2y=xy\\\\xy+2y=1\\\\i.e.\\\\y(x+2)=1\\\\y=(1)/(x+2)`

Hence, inverse function is:

`f(x)=(1)/(x+2)`