Question

Problem: b is any real such that |b| < 1. relation f is defined on any real for which |x| < 1 such that f(x) = (x - b) / (bx - 1). Is this a function??

Answer 1

plug in b=1/2 and see :)

Answer 2

2x-1
-----
x -2

Answer 3

looks functiony

Answer 4

for any given value of x; you only produce 1 y so yeah :)

Answer 5

barring x=2 of course

Answer 6

you can also show f(x) is defined on every point where |x|<1
f(x) is only undefined if bx-1 =0
bx-1 =0
bx=1
b=1/x
since |x|<1 the reciprocal |1/x |>1 but |b| is defined as less than 1 thus b can not equal 1/x and f(x) is defined at every point in the interval |x|<1

Answer 7

how does that define a function? sounds more like continuity.