The graph of the functions f(x) and g(x) are the same
The sketch of the graph of the function
The function is given as:
f(x) = log₂(x)
See attachment for the sketch of the graph.
The domain of f
From the graph, we can see that the x values are greater than 0
This means that the domain of f is x > 0
The equation of f⁻¹(x)
We have:
f(x) = log₂(x)
Rewrite as:
y = log₂(x)
Swap x and y
x = log₂(y)
Express as an exponential function
y = 2ˣ
So, we have:
f⁻¹(x) = 2ˣ
Hence, the equation of f⁻¹(x) is f⁻¹(x) = 2ˣ
The asymptote of f⁻¹(x)
We have:
f⁻¹(x) = 2ˣ
Set the function to 0
f⁻¹(x) = 0
Rewrite as:
y = 0
Hence, the asymptote of f⁻¹(x) is y = 0
How to plot the graph of g(x)?
We have:
f(x) = log₂(x)
g(x) = log₂(x)
Both equations are the same.
Hence, the graph of f(x) and g(x) are the same
Read more about logarithmic functions at:
https://brainly.com/question/3181916
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