Question

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.

Answer 1

Only the equation is a function

Explanation:

we have

`f(x)=x^(2) +8`

Find out the inverse of f(x)

Let

y=f(x)

`y=x^(2) +8`

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

`x=y^(2) +8`

Isolate the variable y

`y^(2)=x-8`

square root both sides

`y=(+/-)√(x-8)`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=(+/-)√(x-8)`

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