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Find the domain of f^-1(x) if f(x)=(x+5)^3

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find the domain
asked Nov 4, 2014 in ALGEBRA 2 by anonymous

1 Answer

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The function f(x) = (x + 5)3  

Change f(x) to y.

y = (x + 5)3

Interchange x and y.

x = (y + 5)3

Now solve for y.

x = (y + 5)3

Apply cube root on each side.

∛x = [∛(y + 5)]3

∛x = y + 5

y = ∛x - 5

Replace y by f-1(x).

f-1(x) =  ∛x - 5

The domain of f-1(x) is { x ∈ R : x ≥ 0 }.

answered Nov 4, 2014 by david Expert

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