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Question
Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.
Options
{3, 2, 1, 0}
{0, −1, −2, −3}
{0, 1, 8, 27}
{0, −1, −8, −27}
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Solution
Let f(x) = x3 be a function with domain {0, 1, 2, 3}. Then domain of f-1 is {0, 1, 8, 27}.
Explanation:
f(x) = x3
Domain = {0, 1, 2, 3}
Range = {03, 13, 23, 33} = {0, 1, 8, 27}
So, f = {(0, 0), (1, 1), (2, 8), (3, 27)}
f-1 = {(0, 0), (1, 1), (8, 2), (27, 3)}
Domain of f-1 = {0, 1, 8, 27}
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