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3 years ago

11

Giao điểm của đường trung trực

1 answer:

slava [35]3 years ago

7 0

Step-by-step explanation:

Đường vuông góc là đường thẳng cắt nhau ở góc vuông. Nếu bạn nhân hệ số góc của hai đường thẳng vuông góc trong mặt phẳng, bạn nhận được −1. Nghĩa là, hệ số góc của các đường vuông góc là các đường nghịch chuyển nhau.

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Find the inverse of the following function. Then prove they are inverses of one another.

solmaris [256]

Answer: $\dfrac{x^2+1}{2}$

Step-by-step explanation:

Given

$f(x)=\sqrt{2x-1}$

We can write it as

$\Rightarrow y=\sqrt{2x-1}$

Express x in terms of y

$\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}$

Replace y be x to get the inverse

$\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}$

To prove, it is inverse of f(x). $f(f^{-1}(x))=x$

$\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x$

So, they are inverse of each other.

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DIA [1.3K]

Answer:

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alexira [117]

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Step-by-step explanation:

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