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Question
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = `(6x - 7)/3`
Solution
f(x) = `(6x - 7)/3`
Let f(x1) = f(x2)
∴ `(6x_1 - 7)/3 = (6x_2 - 7)/3`
∴ x1 = x2
∴ f is a one-one function
f(x) = `(6x - 7)/3` = y (say)
∴ x = `(3"y" + 7)/6`
∴ For every y, we can get x
∴ f is an onto function.
∴ x = `(3y + 7)/6`
= f–1 (y)
Replacing y by x, we get
∴ f–1 (x) = `(3x + 7)/6`
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