Question

Is this statement true? Why?

Answer 1

no, the two are not inverses. I graphed them up on desmos. 

Answer 2

y = tan (x- (pi / 2))
Let's find the inverse function:
We apply arctan to both sides:
arctan (y) = arctan (tan (x- (pi / 2)))
arctan (y) = (x- (pi / 2)
Then, we clear x:
x = arctan (y) + (pi / 2)
Finally we make the change y = x
y = arctan (x) + (pi / 2)
Answer:
False, y = tan ^ -1 (x + (pi / 2)) is not the inverse of y = tan (x- (pi / 2)).
The inverse is:
y= arctan (x) + (pi / 2)