Respuesta :

isyllus

Answer:

Inverse function, [tex]f^{-1}=2^x[/tex]

Step-by-step explanation:

We are given a function [tex]f(x)=\log_2x[/tex]

We need to find the inverse of f(x)

Step 1: Set f(x)=y

[tex]y=\log_2x[/tex]

Step 2: Switch x and y

[tex]x=\log_2y[/tex]

Step 3: Solve for y (isolate y)

[tex]y=2^x[/tex]              [tex]\because \log_ab=x\Rightarrow b=a^x[/tex]

Inverse of function [tex]f(x)\rightarrow f^{-1}(x)=2^x[/tex]


MrRoyal

The inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]

The logarithmic expression is given as:

[tex]f(x) = \log_2(x)[/tex]

Replace f(x) with y

[tex]y = \log_2(x)[/tex]

Swap the positions of x and y

[tex]x = \log_2(y)[/tex]

Apply the change of base rule of logarithm

[tex]2^x = y[/tex]

Rewrite as:

[tex]y = 2^x[/tex]

Express y as an inverse function

[tex]f^{-1}(x) = 2^x[/tex]

Hence, the inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]

Read more about inverse functions at:

https://brainly.com/question/8120556

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