TMUA Practice Question — Worked Solution

P2·Functions, Transformations & Graphs·5.5Mock 0 · P2 · Q12

inequalitiesincreasing functionapplying a function to both sidestranslationreciprocalshifted squaremust-be-true

The real numbers

a

and

b

satisfy

- 1 < a < b < 1.

Consider the following inequalities.

\frac{1}{( a - 1 ) ^{2}} < \frac{1}{( b - 1 ) ^{2}}

a^{2} + a < b^{2} + b

III

\frac{1}{a ^{2} + 1} < \frac{1}{b ^{2} + 1}

Which of the inequalities must be true?

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