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Question
Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1
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Solution
Given f(x) = 2x – 3 ∀ x ∈ R
Now, Leta, b ∈ R such that
f(a) = f(b)
⇒ 2a – 3 = 2b – 3
⇒ a = b
⇒ f(x) is one – one.
Also, If x, y ∈ R such that
f(x) = y
⇒ 2x – 3 = y
⇒ x = `(y + 3)/2` = (y) ∀ y ∈ R
⇒ f(x) is onto and therefore is bijective implies f(x) has an inverse
Let f–1 denote the inverse of f(x) then
f–1(x) = g(x)
= `(x + 3)/2` ∀ x ∈ R
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