Question

2 parts

What is the inverse of f(x) = 6x -24 and second question is


Find the inverse of g(x) = 3x^2 - 5

Answer 1

1)
`f^(-1)(x)=(x)/(6)+4`

2)
`g^(-1)(x)=\sqrt{(x+5)/(3)}`

Explanation:

1) To find the inverse of the function
`f(x) = 6x -24` you need to follow these steps:

- Since
`f(x)=y`, you can rewrite the function:

`y = 6x -24`

- Solve for "x":

`y+24=6x\\\\x=(y+24)/(6)\\\\x=(y)/(6)+4`

- Exchange the variables:

`y=(x)/(6)+4`

Then, the inverse is:

`f^(-1)(x)=(x)/(6)+4`

2) To find the inverse of the function
`g(x) = 3x^2 - 5` you need to follow these steps:

- Since
`g(x)=y`, you can rewrite the function:

`y= 3x^2 - 5`

- Solve for "x":

`y= 3x^2 - 5\\\\(y+5)/(3)=x^2\\\\x=\sqrt{(y+5)/(3)}`

- Exchange the variables:

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

Then, the inverse is:

`g^(-1)(x)=\sqrt{(x+5)/(3)}`

Answer 2

Answer with step-by-step explanation:

1) Inverse of
`f(x) = 6x -24`:

Make the function equal to y to get
`y=6x-24`.

Now making
`x` the subject of the function:

`6x=y+24\\\\x=(y+24)/(6) \\\\x=(y)/(6) +4`

Change back the variable
`y` to
`x` and this is the inverse.

`f'(x)=(x)/(6) +4`

2. Inverse of
`g(x) = 3x^2 - 5`:

Making the function equal to y to get:
`y=3x^2 - 5`

Now making
`x` the subject of the function:

`3x^2=y+5\\\\x^2=(y+5)/(3)`

Taking square root on both sides to get:

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

Change back the variable
`y` to
`x` and this is the inverse.

`g'(x)=\sqrt{(x+5)/(3) }`