It is a relation but not a function
Step-by-step explanation:
Given
(3,6) (3,7) (-2,-5) (-9,11)
First of all we have to define both terms: Relation and Function
A relation is a set of ordered pairs containing one element from each set
A relation can be a function only if there is no repetition in domain i.e. no first element in each ordered pair should be repeated.
In the given set of ordered pairs, they are relation as all the ordered pairs have two values.
While the given relation is not a function, as there is repetition in first elements of two ordered pairs i.e. 3 is repeated in (3,6) (3,7)
Hence,
It is a relation but not a function
Keywords: Functions, Relations
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-5 could not be used in the table again, because we have the value of x=-5 for the value of 15. Therefore correct option is C.
Answer: C. -5
Answer:
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}}](https://tex.z-dn.net/?f=x%3Df%28y%29%5C%5C%5C%5Cx%3D4y%5E4%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B4%7D%3Dy%5E4%5C%5C%5C%5C%5Cpm%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B4%7D%7D%3Dy%5C%5C%5C%5Cf%5E%7B-1%7D%28x%29%3D%5Cpm%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B4%7D%7D)
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.
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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.
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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.
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The attached graph shows the inverse relation (called f₁(x)). It also shows a vertical line intersecting that graph in more than one place.