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nordsb [41]
3 years ago
6

How many cups equals one pint? How many cups equals one pint? 3 following 6 answers 6 Report Abuse Are you sure you want to dele

te this answer? Yes No
Mathematics
1 answer:
Inessa05 [86]3 years ago
8 0
Hello there.

<span>How many cups equals one pint?

2
</span>
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Write a positive or negative integer that represents the situation.
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Create a model to show that 2(2x+3y)=4x+6y
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You would first do 2 multiplied by 2x and that would give you 4x, then you would do 2 multiplied by 3y which would give you 6y, you would put 4x under 2x and put 6y under 3y and bring down your addition symbol 
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3 years ago
Given f(x) = 4x^4 find f^-1(x) Then state whether f^-1(x) is a function.
sdas [7]

Answer:

  • f^{-1}(x)=\pm\sqrt[4]{\dfrac{x}{4}}
  • f^{-1}(x) \quad\text{is not a function}

Step-by-step explanation:

To find the inverse function, solve for y:

x=f(y)\\\\x=4y^4\\\\\dfrac{x}{4}=y^4\\\\\pm\sqrt[4]{\dfrac{x}{4}}=y\\\\f^{-1}(x)=\pm\sqrt[4]{\dfrac{x}{4}}

f(x) is an even function, so f(-x) = f(x). Then the inverse relation is double-valued: for any given y, there can be either of two x-values that will give that result.

___

A function is single-valued. That means any given domain value maps to exactly one range value. The test of this is the "vertical line test." If a vertical line intersects the graph in more than one point, then that x-value maps to more than one y-value.

The horizontal line test is similar. It is used to determine whether a function has an inverse function. If a horizontal line intersects the graph in more than one place, the inverse relation is not a function.

__

Since the inverse relation for the given f(x) maps every x to two y-values, it is not a function. You can also tell this by the fact that f(x) is an even function, so does not pass the horizontal line test. When f(x) doesn't pass the horizontal line test, f^-1(x) cannot pass the vertical line test.

_____

The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.

5 0
3 years ago
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