contestada

Which of the following is true for the relation f(x) = x2 + 8?


Both the equation and its inverse are functions.


Only the inverse is a function.


Only the equation is a function.


Neither the equation nor its inverse is a function.

Respuesta :

calculista

Answer:

Only the equation is a function

Step-by-step explanation:

we have

[tex]f(x)=x^{2} +8[/tex]

Find out the inverse of f(x)

Let

y=f(x)

[tex]y=x^{2} +8[/tex]

Exchange the variables (x for y and y for x)

[tex]x=y^{2} +8[/tex]

Isolate the variable y

[tex]y^{2}=x-8[/tex]

square root both sides

[tex]y=(+/-)\sqrt{x-8}[/tex]

Let

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

[tex]f^{-1}(x)=(+/-)\sqrt{x-8}[/tex]

The inverse function is not a function (because for one input value the function has two different output values)

therefore

Only the equation is a function

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