Respuesta :
Answer:
The correct options are;
1) The functions are inverse of each other and
3) The graphs of the functions are symmetric to each other over the line y = x
Step-by-step explanation:
Here we have
y = 2Ë£ and y = logâ‚‚x
We are to analyze each of the options as follows;
1) The functions are inverse of each other
The above statement is correct as the inverse of y = 2ˣ is x = [tex]2^y[/tex] therefore  y = log₂x is inverse of y = 2ˣ
2) The graphs of the functions are symmetric about the line y = 0
The above statement is not correct as the line y = 0 is the x axis whereby  y = 1 and y = -1 give x = 5 and x = 0.5 respectively
3) The graphs of the functions are symmetric to each other over the line y = x
The line y = x is a straight line with slope = 1  whereby since x >  log₂x, and y > log₂y  then the two lines are symmetric
4) The equation ​ y=log₂x ​ is the logarithmic form of ​ y=2ˣ ​.
The above statement is not correct as log2ˣ = x log2 ≠ log₂x.
The given function are inverse of each other.
The graphs of the functions are symmetric to each other over the line y = x.
Given function are, [tex]y=2^{x}[/tex]  and  [tex]y=log_{2}x[/tex]
    [tex]y=2^{x}\\\\ln(y)=xln2\\\\x=\frac{ln(y)}{ln2}=log_{2}y[/tex]
Therefore, both given function are inverse of each other.
The graphs of the functions are symmetric to each other over the line y = x.
Here, graph is attached below.
From attached graph, it is observed that ,the graphs of the functions are not symmetric about the line y = 0.
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