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)