Select all the numbers that are equivalent.

Mathematics

2 answers:

Pachacha [2.7K]2 years ago

8 0

B,c,d are all equivalent.

xz_007 [3.2K]2 years ago

5 0

B,C,D are all equivalent.

You might be interested in

Is the function even, odd or neither?<br> y=x^2-2x-8

mestny [16]

It is neither.

To be even, f(x) must equal f(-x).

If you substitute -x for x, you'd get

y = (-x)^2 - 2(-x) -8

y = x^2 +2x -8

This is not the same as the original, so this is not even.

To be odd, f(x) must equal -f(-x).

If you take the -x substitution from the last step and then multiply it by -1, you'd have:

y = -1 (x^2 +2x -8)

y = -x^2 -2x +8

This is not the same as the original either.

The function is neither even nor odd.

5 0

1 year ago

Read 2 more answers

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.