anonymous
  • anonymous
what is the inverse of the function y=5x^3?
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
To find the inverse: Replace f(x) with y Switch x's and y's, so put x where y is and x where y is. Solve for y Replace y with f^-1(x)
anonymous
  • anonymous
\[y=5x^3 \implies x = 5y^3\] solve for y now
anonymous
  • anonymous
so would it y=5x/3?

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anonymous
  • anonymous
No where did you get the 3
anonymous
  • anonymous
\[y^3 = \frac{ x }{ 5 }\] you will have to take the cube root not divide by 3.
anonymous
  • anonymous
\[\huge x^{1/3} = \sqrt[3]{x}\] cube root
anonymous
  • anonymous
\[\sqrt[3]{5x}\]
anonymous
  • anonymous
so it would be that ^ correct?
anonymous
  • anonymous
Nope, you take the cube root of both sides, \[\huge y^3 = \frac{ x }{ 5 } \implies y = \sqrt[3]{\frac{ x }{ 5 }} \implies f^{-1}(x) = \sqrt[3]{\frac{ x }{ 5 }}\]
anonymous
  • anonymous
\[\large y^3 = \frac{ x }{ 5 } \implies y = \sqrt[3]{\frac{ x }{ 5 }} \implies f^{-1}(x) = \sqrt[3]{\frac{ x }{ 5 }}\]
anonymous
  • anonymous
thank you !!

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