Answer:
The inverse of f(x) is
[tex]f^{-1} (x) = \frac{2 x+3}{4}[/tex]
Step-by-step explanation:
Explanation:-
Given [tex]f(x) = \frac{4 x-3}{2}[/tex]
Inverse of f(x)
f(x) is a one-one function
let f(x₁) and f(x₂) be two functions are
[tex]f(x_{1} ) = \frac{4 x_{1} -3}{2}[/tex]
[tex]f(x_{2} ) = \frac{4 x_{2} -3}{2}[/tex]
⇒ [tex]\frac{4 x_{1} -3}{2} = \frac{4 x_{2} -3}{2}[/tex]
⇒ 4 x₁ - 3 = 4 x₂ - 3
⇒ 4 x₁ = 4 x₂
⇒ x₁ = x₂
Given function is one-one function
y = f(x) = [tex]\frac{4 x-3}{2}[/tex]
⇒ 2 y = 4 x - 3
⇒ 4 x = 2 y + 3
⇒ [tex]x = \frac{2 y + 3}{4}[/tex]
⇒ f⁻¹(x) [tex]= \frac{2 y + 3}{4}[/tex]
Given function f(x) is onto function
Therefore f(x) is one-one and onto function
[tex]f^{-1} (x) = \frac{2 x+3}{4}[/tex]
