austinsrennie austinsrennie
  • 30-03-2022
  • Mathematics
contestada

Consider the function f(x)=8x3−2. If f(g(x))=x and g(f(x))=x, find g(x)

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aryanputhran
aryanputhran aryanputhran
  • 30-03-2022

I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.

For this problem, simply find the inverse of f(x).

If you are stuck, I could provide you with a solution below...

f(x) = 8x³ - 2

y = 8x³ - 2

y + 2 = 8x³

(y + 2)/8 = x³

cube root((y + 2)/8) = x

g(x) = cube root((x + 2)/8)

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