Question

Sketch the graph of f(x) = log2x

Answer 1

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:

brainly.com/question/3181916

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