Question

What is the answer for this one ?

Answer 1

Option B:

`$f^(-1)(x)=(3-x)/(14)`

Solution:

Given function is
`f(x)=3-14 x`.

To find the inverse of the function:

Let y = f(x)

`y=3-14 x`

Subtract 3 on both sides of the equation, we get

`y-3=-14 x`

Divide by –14 on both sides of the equation.

`$(y-3)/(-14) =(-14x)/(-14)`

`$(y-3)/(-14) =x`

Negative sign in the denominator go to the numerator , we get

`$(3-y)/(14) =x`

We know that y = f(x) ⇒
`x=f^(-1)(y)`

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

`$(3-y)/(14) =f^(-1)(y)`

Since the choice of the variable is arbitrary, we can write this as

`$(3-x)/(14) =f^(-1)(x)`

`$f^(-1)(x)=(3-x)/(14)`

Hence Option B is the correct answer.