The graph of y = cos x is reflected in the line x = π/2 and then in the line y = 3. Find the equation of the resulting function.

Answer 1

cosx reflected over x=pi/2 is the same as reflecting cosx over the x axis or y=0,

which just switches y with -y

-y=cosx

or

y=-cosx

then reflect over y=3

that flips the graph upside down, switching y and -y again, back to cosx

but also shifting the curve up by 2x3 =6

what used to be a minimum -1 is now a maximum 7, with new midline =6

it becomes y=cosx +6