Given that g(x) = x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1, find g^-1(x).

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25-10-2017
Mathematics

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Given that g(x) = x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1, find g^-1(x).

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wizard123 wizard123 · Answer 1 · 2017-10-25T04:25:58+02:00

wizard123 wizard123

25-10-2017

First Factor.

[tex](x-1)^5 = x^5 -5x^4+10x^3 -10x^2+5x-1[/tex]

[tex]g(x) = y = (x-1)^5[/tex]

Find inverse by solving for 'x'

[tex]x-1 = y^{1/5} \\ \\ x = y^{1/5} +1 \\ \\ g^{-1} (x) = x^{1/5} + 1[/tex]

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