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Question
Answer the following:
A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1
Solution
f(x) = `(3x)/5 + 2`, x ∈ R
Let f(x1) = f(x2)
∴ `(3x_1)/5 + 2 = (3x_2)/5 + 2`
∴ x1 = x2
∴ f is a one-one function
Let f(x) = `(3x)/5 + 2` = y (say), y ∈ R
∴ x = `(5(y - 2))/3`
∴ for every y ∈ R, there is some x ∈ R
∴ f is an onto function.
x = `(5(y - 2))/3` = f–1 (y)
∴ f–1 (x) = `(5(x - 2))/3`
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