What is the inverse function of $f (x) = 5 x^{3} + 4 x^{2} + 3 x + 4$ $f(x) =5x^3 + 4x^2 + 3x + 4$ ?

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What is the inverse function of $f (x) = 5 x^{3} + 4 x^{2} + 3 x + 4$ $f(x) =5x^3 + 4x^2 + 3x + 4$ ?

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Answer 1 · 2016-01-02T01:20:39

$x = 5 y^{3} + 4 y^{2} + 3 y + 4$ $x=5y^3+4y^2+3y+4$

Explanation:

The simplest way to write the inverse function is to write $y$ $y$ in place of $f (x)$ $f(x)$ and switch all the $x$ $x$ s with $y$ $y$ s and the $y$ $y$ with $x$ $x$ , giving:

$x = 5 y^{3} + 4 y^{2} + 3 y + 4$ $x=5y^3+4y^2+3y+4$

This can be written explicitly (in terms of $y$ $y$ ), but it uses the incredibly cumbersome cubic formula and is overall unhelpful. But, for the sake of interest, it's as follows:

$x = - \frac{{(15 \sqrt{3} \sqrt{675 y^{2} - 4576 y + 7900} - 675 y + 2288)}^{\frac{1}{3}}}{15 (2^{\frac{1}{3}})} + \frac{29 (2^{\frac{1}{3}})}{15 {(15 \sqrt{3} \sqrt{675 y^{2} - 4576 y + 7900} - 675 y + 2288)}^{\frac{1}{3}}} - \frac{4}{15}$ $x=-(15 sqrt(3) sqrt(675 y^2-4576 y+7900)-675 y+2288)^(1/3)/(15 (2^(1/3)))+(29 (2^(1/3)))/(15 (15 sqrt(3) sqrt(675 y^2-4576 y+7900)-675 y+2288)^(1/3))-4/15$

Graph:
![http://www.wolframalpha.com/input/?i=y%3D5x^3%2B4x^2%2B3x%2B4+inverse]( useruploads.socratic.org )

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What is the inverse function of $f (x) = 5 x^{3} + 4 x^{2} + 3 x + 4$ $f(x) =5x^3 + 4x^2 + 3x + 4$ ?

1 Answer

Explanation:

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What is the inverse function of f(x)=5x3+4x2+3x+4f(x) =5x^3 + 4x^2 + 3x + 4?

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What is the inverse function of $f (x) = 5 x^{3} + 4 x^{2} + 3 x + 4$ $f(x) =5x^3 + 4x^2 + 3x + 4$ ?