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marissa [1.9K]
3 years ago
14

Help please!!!!!!!! It’s pre cal

Mathematics
2 answers:
tino4ka555 [31]3 years ago
6 0

Answer:

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

Step-by-step 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\sqrt{x-3}

h^{-1}(x)=\pm\sqrt{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.

11111nata11111 [884]3 years ago
6 0

Answer:

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

Step-by-step explanation:

h(x) = x² + 3

y = x² + 3

y - 3 = x² ⇒  x² = y - 3

\sqrt{x^{2} } = \sqrt{y-3} \\x =  \sqrt{y - 3} , -\sqrt{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

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