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Question
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = 9x3 + 8
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Solution
f(x) = 9x3 + 8
Let f(x1) = f(x2)
∴ 9x13 + 8 = 9x23 + 8
∴ x1 = x2
∴ f is a one-one function.
f(x) = 9x3 + 8 = y, (say)
∴ x = `root(3)((y - 8)/9)`
∴ For every y we can get x.
∴ f is an onto function.
∴ x = `root(3)((y - 8)/9)`
= f–1 (y)
Replacing y by x, we get
f–1 (x) = `root(3)((x - 8)/9)`
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