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bonufazy [111]
3 years ago
8

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

Mathematics
1 answer:
solmaris [256]3 years ago
8 0

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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Answer:

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Solution:

<u>Note that:</u>

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A store is having a sale on almonds and jelly beans. For 3 pounds of almonds and 5 pounds of jelly beans, the total cost is $19
yaroslaw [1]

Answer:

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Step-by-step explanation:

A: almond

J: jelly bean

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