TMUA Practice Question — Worked Solution

P2·Functions, Transformations & Graphs·6.5CrackTMUA Original

functional-equationsymmetryanti-periodicitymust-be-truemulti-statementcounterexample

A function

f

is defined for all real numbers and satisfies both

f (2 - x) = f (x) and f (x + 3) = - f (x)

for every real number

x

f (\frac{5}{2}) = 0

f (x + 6) = f (x)

for every real number

x

III

f (1) = 0

Which of the above must be true?

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