TMUA Official 2019 Paper 2 · Question 20

When the graph of the function $y=f(x)$ , defined on the real numbers, is reflected in the $y$ -axis and then translated by 2 units in the negative $x$ -direction, the result is the graph of the function $y=g(x)$ .

When the graph of the same function $y=f(x)$ is translated by 2 units in the negative $x$ -direction and then reflected in the $y$ -axis, the result is the graph of the function $y=h(x)$ .

Which one of the following conditions on $y=f(x)$ is necessary and sufficient for the functions $g(x)$ and $h(x)$ to be identical?

f(x)=f(x+2)

for all

x

f(x)=f(x+4)

for all

x

f(x)=f(x+8)

for all

x

f(x)=f(-x)

for all

x

f(x)=f(2-x)

for all

x

f(x)=f(4-x)

for all

x

f(x)=f(8-x)

for all

x

examday

Official 2019 Paper 2 · Q20