Verified Answer :

subediprashant

y = 1/2x + 3
change x and y

x = 1/2y + 3
now find the value of y and that is inverse function 

x - 3 =1/2 y
y = 2x- 6
 
f-(x) = 2x - 6


for both domain : ( - ∞ , + ∞ )

range f (x) : ( - ∞ , + ∞ )  - { 0 }
range f-(x) :( -∞ , +∞)

To find the inverse function you need to change \(f(x)\) (call it \(y\)) and \(x\), then solve for \(y\):

\(y = \frac{1}{2}x+3 \\ x = \frac{1}{2}y + 3 \\ x - 3 = \frac{1}{2}y \\ 2x-6 = y\)

So now you have \(f^{-1}(x) = 2x-6\).

Composition to prove inverse relation: \(f \circ f^{-1} (x) = x\):

\(f(f^{-1}(x)) = \frac{1}{2}(2x-6)+3 = x - 3 + 3 = x \square\)

Domain and Range of both functions is Real numbers since they are both linear equations.