3x0.2 help pleases.w
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The graph of the functions f(x) and g(x) are the same
<h3>The sketch of the graph of the function</h3>The function is given as:
f(x) = log₂(x)
See attachment for the sketch of the graph.
<h3>The domain of f</h3>From the graph, we can see that the x values are greater than 0
This means that the domain of f is x > 0
<h3>The equation of f⁻¹(x)</h3>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
<h3>The asymptote of f⁻¹(x)</h3>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
<h3>How to plot the graph of g(x)?</h3>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:
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