Respuesta :

Hello!

We have the function f(x) = 3x.

The first step is to calculate the inverse function of f(x):

First, let's replace where's f(x) by y:

f(x) = 3x

y = 3x

Now, let's swap the values of x and y:

y = 3x

x = 3y

Now we have to solve it to obtain y:

3y = x

y = x/3

So, we will have:

[tex]f(x)^{-1}=\frac{x}{3}[/tex]

B. Reasoning:

[tex]\begin{gathered} f(f^{-1}(x))=(3(\frac{x}{3})=x \\ \\ f^{-1}(f(x))=\frac{3x}{3}=x \end{gathered}[/tex]

Image with the reasoning:

So, these equations are correct.

As it has no restrictions, this function is valid for all values of x.

Right answer: alternative A.

Obs: You'll have to type in the first box: x/3.

Ver imagen CheoR597566
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