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Given f(x) = 3x - 5, find the inverse function f⁻¹(x).

1. f⁻¹(x) = 1/(3x - 5)
2. f⁻¹(x) = (x + 5)/3
3. f⁻¹ does not exist because f is not one-one
4. f⁻¹ does not exist because f is not onto

Correct answer: f⁻¹(x) = (x + 5)/3

Solution

Swap and solve: y = 3x - 5 gives x = (y + 5)/3, hence f⁻¹(x) = (x + 5)/3. The function is one-one and onto on R.

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