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Find the inverse function of $f(x) = x^3 +1.$
asked in Set Theory & Algebra by Boss (10.8k points) | 38 views

2 Answers

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Given $f(x)= x^3 + 1$

Let $y=f(x)$

$y=x^3+1$

$x=y^3+1$

$y^3=x-1$

$ y=\sqrt[3]{x-1}$
answered by Junior (659 points)
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The inverse of function:

  • $f$ is a bijection ,$f_{A\rightarrow B}$
  • $f^{-1}$ is a bijection ,$f_{B\rightarrow A}$
  • $f^{-1}_{B\rightarrow A}(x) = y$   iff  $f_{A\rightarrow B}(y) = x$

Given that $f(x) = x^{3} + 1$

$f^{-1}(x) = y \ $ iff $\ f(y) = x$

$\implies y^{3} + 1 = x$

$\implies y^{3} = x - 1$

$\implies y = \sqrt[3]{x-1}$

answered by Boss (41.8k points)

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