Year 11 Maths - Methods Functions and Relations

One-to-one Functions and Implied Domains

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Questions

Question 1

28519

Which of the functions is not one-to-one?

\(y = \sqrt {x - 1} \)

\(y = {x^2} - 1\)

\(y = {x^3} - 1\)

\(y = \dfrac{1}{{x - 1}}\)

Answer

\(y = {x^2} - 1\)

Worked Solution

\(y=x^{2}-1\) is a parabola, so it is not one-to-one.
The square root function \(y=\sqrt{x-1}\), the cubic function \(y=x^{3}-1\) and the hyperbola \(y=\dfrac{1}{x-1}\) are all one-to-one. \(\quad \because B\)

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