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r-ruslan [8.4K]
4 years ago
15

Identify the solution set of the inequality using the given replacement set.

Mathematics
1 answer:
LenKa [72]4 years ago
5 0
-10 < -7 \to true \\&#10;-7.2 < -7 \to true \\&#10;-7 < -7 \to not \ true \\&#10;-6.9 < -7 \to not \ true \\&#10;6.5 < -7 \to not \ true \\&#10;9 < -7 \to not \ true \\ \\&#10;\{-10,-7.2 \} \Rightarrow \hbox{the answer is A}
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If G^-1(x) is the inverse of G(x), what is the value of G^-1(G(x))?
Ber [7]

Answer:

G^{-1}(G(x))=x

Step-by-step explanation:

Definition: Let f be one-to-one function with the domain A and  the range B. Then the inverse function f^{-1} has the domain B and the range A and is defined as

f^{-1}(y)=x\ \Leftrightarrow \ f(x)=y

Facts:

1) For every x\in A:

f^{-1}(f(x))=x

2) For every y\in B:

f(f^{-1}(y))=y

So, G^{-1}(G(x))=x

5 0
4 years ago
Aurelio Espinoza buys a computer disk file for 14.95 , a surge protector for 19.95 and 2 boxes of labels for 19.99 each . The sa
vodomira [7]
I believe it is 71. 8848
5 0
3 years ago
Martha paid $42.40 for her sister’s birthday present. This included 6% sales tax. What was the cost of the gift before tax? A. $
kifflom [539]
I think the answer is 40.00

4 0
3 years ago
1/2+2/3+1/6 equals what
Anastasy [175]

Answer:

4/11

Step-by-step explanation:

Add them together

6 0
4 years ago
Read 2 more answers
Question 5: prove that it’s =0
mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that \cos(\frac{2}{x}) is a variable number between -1 and 1 (inclusive).

This means that -1 \le \cos(\frac{2}{x}) \le 1.

x^4 \ge 0 for all value x. So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4

By squeeze theorem, if  -x^4 \le x^4 \cos(\frac{2}{x}) \le x^4

and \lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L, then we can also conclude that \im_{x \rightarrow} x^4\cos(\frac{2}{x})=L.

So we can actually evaluate the "if" limits pretty easily since both are continuous  and exist at x=0.

\lim_{x \rightarrow 0}x^4=0^4=0

\lim_{x \rightarrow 0}-x^4=-0^4=-0=0.

We can finally conclude that \lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0 by squeeze theorem.

Some people call this sandwich theorem.

6 0
3 years ago
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