Question

Write the inverse of the logarithmic function used to represent the situation in model 1, . Express the answer in radical form.

Answer 1

Answer:

The inverse of  logarithmic function

f⁻¹(x)  $= 2^{x}$  

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)

⇒  $log_{2} x_{1} = log_{2} x_{2}$

⇒  x ₁ = x₂

Therefore f(x) is one-one function

Let y = f(x) = log₂ˣ

  ⇒  y =  log₂ˣ

 ⇒  $x = 2^{y}$  

f(x) is a one-one function and onto

⇒  $x = 2^{y}$  

⇒ f⁻¹(x)  $= 2^{y}$  

The inverse of  logarithmic function

f⁻¹(x)  $= 2^{x}$