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Talja [164]
2 years ago
15

Help please with question 7!!

Mathematics
1 answer:
elena-14-01-66 [18.8K]2 years ago
6 0
Look at the picture I inserted for the answer, hopes this helps

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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
What are the steps to(2x+3y)4
lilavasa [31]
(2x + 3y)4

Distribute 

4*2x = 8x
4*3y = 12y

8x + 12y 

Answer: 8x + 12y
8 0
3 years ago
Read 2 more answers
Domain and, range in interval notation
Bas_tet [7]

Domain: [-4,4]  (left-to-right or x-values used)

Range: [-4,4] (down-to-up or y-values used)

Function: no

4 0
2 years ago
Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does
sveta [45]
<span>A physical property is that it is a white metal. The other descriptions are all chemcial properties such as how it reacts and conducts. Density could also be another answer as it is also physical.</span>
7 0
3 years ago
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2.865 in expanded form
kirill [66]

Answer: 2.865

Step-by-step explanation:

4 0
3 years ago
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