Answer:
The inverse of logarithmic function
f⁻¹(x) [tex]= 2^{x}[/tex]
Step-by-step explanation:
Explanation:-
Given f(x) = log₂ˣ ( 2 is a radical)
Let x₁ and x₂ be the ∈ domain f
⇒f(x₁) = f(x₂)
⇒ [tex]log_{2} x_{1} = log_{2} x_{2}[/tex]
⇒ x ₁ = x₂
Therefore f(x) is one-one function
Let y = f(x) = log₂ˣ
⇒ y = log₂ˣ
⇒ [tex]x = 2^{y}[/tex]
f(x) is a one-one function and onto
⇒ [tex]x = 2^{y}[/tex]
⇒ f⁻¹(x) [tex]= 2^{y}[/tex]
The inverse of logarithmic function
f⁻¹(x) [tex]= 2^{x}[/tex]