Respuesta :

calculista

Answer:

[tex]f^{-1} (x)=\frac{1}{5}x[/tex]

Step-by-step explanation:

we have

[tex]f(x)=5x[/tex]

Let

y=f(x)

[tex]y=5x[/tex]

Exchange the variables x for y and y for x

[tex]x=5y[/tex]

isolate the variable y

[tex]y=x/5[/tex]

Let

[tex]f^{-1} (x)=y[/tex]

[tex]f^{-1} (x)=\frac{1}{5}x[/tex]

Answer:

Option c

Step-by-step explanation:

Give that f(x) = 5x

We have to choose among the four options which is the inverse of f

Let us try directly from f(x)

[tex]f(x) = 5xy =5x[/tex]

Divide both sides by 5

[tex]x = \frac{y}{5}

Verify:

Let us do composiition of function as

\\[tex]f(f^{-1} (x))=f(\frac{1}{5}x)\\ =5(\frac{1}{5}x)\\\\=x[/tex]=\frac{1}{5} x[/tex]

WE find that our answer is right

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