Engineering
Mathematics
Inverse of a Function
Question
If f : [0, 5] → [7, 13] be a surjective linear map such that f (1) > f(2) and f (2α2 – α – 1) + 13 = f(α2 + 1) + f(0) for some α ∈ [0, 5], then find the value of f –1(α + 5).
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Solution
Clearly f is one-one & decreasing ⇒ f(5) = 7, f(0) = 13
f(2α2 – α – 1) = f(α2 + 1) ⇒ α = –1, 2
since α [0, 5] ⇒ α = 2
⇒ f –1 (α + 5) = f–1 (7) = 5.