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spayn [35]
3 years ago
8

PLEASE SOMEONE HELP I TRULY DO NOT UNDERSTAND

Mathematics
1 answer:
IceJOKER [234]3 years ago
7 0

Hi there!

\large\boxed{f^{-1}(x) =  \sqrt[3]{\frac{x+4}{9} } }

f(x) = 9x^{3} - 4

Find the inverse by replacing f(x) with y and swapping the x and y variables:

x = 9y^{3} - 4

Isolate y by adding 4 to both sides:

x + 4 = 9y^{3}

Divide both sides by 9:

\frac{x+4}{9}= y^{3}

Take the cube root of both sides:

y = \sqrt[3]{\frac{x+4}{9} }\\\\f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} }

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