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Question
Verify that f and g are inverse functions of each other, where f(x) = x3 + 4, g(x) = `root(3)(x - 4)`
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Solution
f(x) = x3 + 4
Replacing x by g(x), we get
f[g(x)] = [g(x)]3 + 4
= `(root(3)(x - 4))^3 + 4`
= x – 4 + 4
= x
g(x) = `root(3)(x - 4)`
Replacing x by f(x), we get
g[f(x)] = `root(3)("f"(x) - 4)`
= `root(3)(x^3 + 4 - 4)`
= `root(3)(x^3)`
= x
Since, f[g(x)] = x and g[f(x)] = x.
∴ f and g are inverse functions of each other.
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