Find the inverse of the following function. Then prove they are inverses of one another. f (x)= root 2x-1.

Question

Find the inverse of the following function. Then prove they are inverses of one another.
f (x)= root 2x-1.

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Doris 3 years 2021-08-18T23:12:43+00:00 1 Answers 14 views 0

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  1. Acacia
    0
    2021-08-18T23:13:53+00:00
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    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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