Question

Find the inverse of the function.

f(x) = 4x^3 - 7

Answer 1

@jim_thompson5910

Answer 2

The basic idea is to replace f(x) with y, swap x and y, then solve for y to get the inverse.


Similar Example (just with different numbers)


\[\Large f(x) = 19x^3 + 2\]


\[\Large y = 19x^3 + 2\]


\[\Large x = 19y^3 + 2\]


\[\Large x-2 = 19y^3\]


\[\Large 19y^3 = x-2\]


\[\Large y^3 = \frac{x-2}{19}\]


\[\Large y = \sqrt[3]{\frac{x-2}{19}}\]


\[\Large f^{-1}(x) = \sqrt[3]{\frac{x-2}{19}}\]


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So the inverse of \(\Large f(x) = 19x^3 + 2\) is \(\Large f^{-1}(x) = \sqrt[3]{\frac{x-2}{19}}\)

Answer 3

so it would be \[\sqrt[3]{\frac{ x+7 }{ 4 }}\]

Answer 4

correct