Question

If, F(x)=2x/7 +4, witch of the following is the inverse

Answer 1

Given:

The function is

`F(x)=(2)/(7)x+4`

To find:

The inverse function of the given function.

Solution:

We have,

`F(x)=(2)/(7)x+4`

Putting F(x)=y, we get

`y=(2)/(7)x+4`

Interchange x and y.

`x=(2)/(7)y+4`

Subtract 4 from both sides.

`x-4=(2)/(7)y`

Multiply both sides by 7.

`7(x-4)=2y`

`7x-28=2y`

Divide both sides by 2.

`(7x-28)/(2)=y`

`(7)/(2)x-14=y`

`y=(7)/(2)x-14`

Putting
`y=F^(-1)(x)`, we get

`F^(-1)(x)=(7)/(2)x-14`

Therefore, the required inverse function is
`F^(-1)(x)=(7)/(2)x-14`.