Question

Help please!!!!!!!! It’s pre cal

Answer 1

a. No, the inverse function does not pass horizontal line test

Explanation:

h(x) = x² + 3

y = x² + 3

y - 3 = x² ⇒ x² = y - 3

`\sqrt{x^(2) } = √(y-3) \\`
`</p><p>x =  √(y - 3) , -√(y-3)`

h^{-1} x = \sqrt{x - 3} , -\sqrt{x-3}[/tex]

The function h^{-1} x fails the horizontal line test, it is not a one to one function.

So, option a is correct

Answer 2

No, the inverse function does not pass the vertical line test.

Explanation:

Remember that
`h(x)=y`. To find the inverse of our function we are going to invert x and y and solve for y:

`h(x)=x^2+3`

`y=x^2+3`

`x=y^2+3`

`x-3=y^2`

`y=\pm√(x-3)`

`h^(-1)(x)=\pm√(x-3)`

Now we can graph our function an perform the vertical line test (check the attached picture).

Remember that the vertical line test is a visual way of determine if a relation is a function. A relation is a function if and only if it only has one value of y for each value of x. In other words, a relation is a function if a vertical line only intercepts the graph of the function once.

As you can see in the picture, the vertical line x = 15 intercepts the function twice, so the inverse function h(x) is not a function.

We can conclude that the correct answer is: No, the inverse function does not pass the vertical line test.