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Colt1911 [192]
3 years ago
14

Write inequalities WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
7 0

1.

84-12x<=18 (that is a less than or equal to)

2.

4+x<=15

3.

500<=363+x

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Find g^-1(x) <br><br> A<br> B<br> C<br> D
Katyanochek1 [597]
<h2>Answer:</h2>

a. \ g^{-1}=-1 \pm\sqrt{\frac{3}{x}+1}

<h2>Step-by-step explanation:</h2>

A function has an inverse function if and only if passes the Horizontal Line Test for Inverse Functions. This test tells us that a function f has an inverse function if and only if there is no any horizontal line that intersects the graph of f at more than one point. So the function is called one-to-one. The graph of g is shown below. As you can see, this function does not pass the Horizontal Line Test, therefore the inverse is not a function. However, let's find g^-{1}(x):

g(x)=\frac{3}{x^2+2x} \\ \\ Substitute \ g(x) \ by \ y \\ \\y=\frac{3}{x^2+2x} \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{3}{y^2+2y} \\ \\ Solve \ for \ y: \\ \\y^2+2y=\frac{3}{x} \\ \\ Completing \ square \\ \\y^2+2y\mathbf{+ 1}\mathbf{-1}=\frac{3}{x} \\ \\(y+1)^2=\frac{3}{x}+1 \\ \\y+1=\pm\sqrt{\frac{3}{x}+1} \\ \\ y=-1 \pm\sqrt{\frac{3}{x}+1}

Finally, substitute y \ by \ g^{-1}:

boxed{g^{-1}=-1 \pm\sqrt{\frac{3}{x}+1}}

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Answer:

Susan B Anthony, Champion of temperance, abolition, the rights of labor, and equal pay for equal work, Susan Brownell Anthony became one of the most visible leaders of the women's suffrage movement. Along with Elizabeth Cady Stanton, she traveled around the country delivering speeches in favor of women's suffrage.

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