Suppose that \( f(x) = \frac{1} { 2x + b}. \) For what value of b does \( f ^-1(x) = \frac{1-2x} { 2x}?\)
+130071 f(x) = 1 / [2x + b]
Let's find the inverse
For f(x) write y
y = 1 /[ 2x + b ] multiply both sides by 2x + b
y ( 2x + b) = 1
2xy + yb = 1
2xy = 1 - yb
x = [ 1 - yb] / [2y] "swap" x and y
y = [ 1 - bx] / [ 2x] for y, write f-1(x)
f-1(x) = [ 1 - bx ] / [ 2x ]
So....it's obvious that b = 2
