Finding the inverse of a quadratic function?

In summary, the problem involves simplifying an expression using the square root function and the distributive property. The 1/2 outside of the square root function comes from moving the 1/2 out of the expression (x+3)/-2. The final step involves multiplying both the numerator and denominator by -2 inside the square root.
  • #1
SoConfused__
23
0
Hello, I am sorry for removing the template but it is not an actual problem that I need help with. Well it is, but it should be pretty quick and straight forward.

The problem is located here: http://www.cdli.ca/courses/math3103/unit05_org01_ilo04/images/3-less9.gif

(It's a bit difficult to type out.)

I'm having difficulty with only 1 step that I need straightened out.

On the second last line, where did the 1/2 outside of the square root function come from? And Why does it appear there? I am thinking the 1/2 just got moved out of it, because it was under x+3.

Please help, thank you so much.
 
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  • #2
They wrote (x+3)/-2=(x+3)*2/((-2)*2)=(2x+6)/(-4)=(1/4)*((2x+6)/(-1))=(1/4)*(-2x-6). Then they took sqrt(1/4)=1/2 and moved that out.
 
  • #3
Multiply both numerator and denominator by -2 inside the square root

[tex] y + 1 = \pm \sqrt{\frac{-2(x + 3)}{- 2 (-2)}[/tex]
 
  • #4
Multiply both numerator and denominator by -2 inside the square root

[tex] y + 1 = \pm \sqrt{\frac{-2x-6}{4}[/tex]
 

1. What is the inverse of a quadratic function?

The inverse of a quadratic function is a function that "undoes" the original quadratic function. It is a reflection of the original function over the line y=x, meaning that the input and output values of the original function are switched in the inverse function.

2. How do you find the inverse of a quadratic function?

To find the inverse of a quadratic function, you can use the following steps:
1. Start with the original quadratic function, which is in the form y = ax^2 + bx + c.
2. Replace y with x and x with y.
3. Solve for y to get the inverse function.
4. Check your answer by verifying that the inverse function is a reflection of the original function over the line y=x.

3. What is the domain and range of the inverse of a quadratic function?

The domain of the inverse of a quadratic function is the range of the original function, and the range of the inverse function is the domain of the original function. In other words, the x-values of the inverse function are the y-values of the original function, and the y-values of the inverse function are the x-values of the original function.

4. Can every quadratic function have an inverse?

Not every quadratic function has an inverse. For a function to have an inverse, it must pass the horizontal line test, which means that no horizontal line can intersect the graph of the function more than once. If a quadratic function has a horizontal line of symmetry, it will not have an inverse.

5. How can finding the inverse of a quadratic function be useful?

Finding the inverse of a quadratic function can be useful in many ways. It can help solve equations involving quadratic functions, graph the inverse function to find the domain and range of the original function, and model real-world situations where the input and output values are related in a quadratic way. It can also be used to find the inverse of other types of functions, such as exponential or logarithmic functions.

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