TMUA 2018 Paper 2 Q10 — Worked Solution

P2·Functions, Transformations & Graphs, Logic & Quantifiers·6.0Official · 2018 · Q10

reflection-symmetryfunction-equationsnecessary-and-sufficient

The function

f (x)

is defined for all real numbers. Consider the following three conditions, where

a

is a real constant:

f (a - x) = f (a + x)

for all real

x

f (2 a - x) = f (x)

for all real

x

III

f (a - x) = f (x)

for all real

x

Which of these conditions is/are necessary and sufficient for the graph of

y = f (x)

to have reflection symmetry in the line

x = a

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