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Question
Verify that f and g are inverse functions of each other, where f(x) = `(x - 7)/4`, g(x) = 4x + 7
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Solution
f(x) = `(x - 7)/4`, g(x) = 4x + 7
f[g(x)] = `(g(x) -7)/4`
=` (4x + 7 - 7)/4`
= x
f[g(x)] = f(4x + 7)
Replacing x by f(x), we get
`g[f(x)]= 4f(x) + 7= 4((x - 7)/4) + 7 = x`
∴ f and g are inverse functions of each other.
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