Question

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

Answer 1

The inverse of logarithmic function

f⁻¹(x)
`= 2^(x)`

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)`