gemalopez065 gemalopez065
  • 15-12-2021
  • Mathematics
contestada

f(x)= -2x^3-6

Determine whether the inverse of f is a function. Then find the inverse.

fx 2x36 Determine whether the inverse of f is a function Then find the inverse class=

Respuesta :

garyimmanuel garyimmanuel
  • 15-12-2021

Answer: [tex]f^{-1}(x) = \sqrt[3]{\frac{x+6}{(-2)} }[/tex]

The inverse of f is a function

Step-by-step explanation:

[tex]f(x) = -2x^{3}-6\\f^{-1}(x) = y = -2x^{3}-6\\y + 6 = -2x^{3}\\\frac{y+6}{-2} = x^{3}\\x = \sqrt[3]{\frac{y+6}{(-2)} } \\f^{-1}(y) = \sqrt[3]{\frac{y+6}{(-2)} } \\So, f^{-1}(x) = \sqrt[3]{\frac{x+6}{(-2)} }[/tex]

The inverse of f is a function since every single x only has 1 answer for y

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