Question

What is the answer for this one ?

Answer 1

Option B:

$f^{-1}(x)=\frac{3-x}{14}$

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.

$\frac{y-3}{-14} =\frac{-14x}{-14}$

$\frac{y-3}{-14} =x$

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

$\frac{3-y}{14} =x$

We know that y = f(x)   ⇒ $x=f^{-1}(y)$

Substitute $x=f^{-1}(y)$

$\frac{3-y}{14} =f^{-1}(y)$

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

$\frac{3-x}{14} =f^{-1}(x)$

$f^{-1}(x)=\frac{3-x}{14}$

Hence Option B is the correct answer.