Option B:
[tex]$f^{-1}(x)=\frac{3-x}{14}[/tex]
Solution:
Given function is [tex]f(x)=3-14 x[/tex].
To find the inverse of the function:
Let y = f(x)
[tex]y=3-14 x[/tex]
Subtract 3 on both sides of the equation, we get
[tex]y-3=-14 x[/tex]
Divide by –14 on both sides of the equation.
[tex]$\frac{y-3}{-14} =\frac{-14x}{-14}[/tex]
[tex]$\frac{y-3}{-14} =x[/tex]
Negative sign in the denominator go to the numerator , we get
[tex]$\frac{3-y}{14} =x[/tex]
We know that y = f(x) ⇒ [tex]x=f^{-1}(y)[/tex]
Substitute [tex]x=f^{-1}(y)[/tex]
[tex]$\frac{3-y}{14} =f^{-1}(y)[/tex]
Since the choice of the variable is arbitrary, we can write this as
[tex]$\frac{3-x}{14} =f^{-1}(x)[/tex]
[tex]$f^{-1}(x)=\frac{3-x}{14}[/tex]
Hence Option B is the correct answer.
