Assume that f is a one-to-one function

Question

Assume that f is a one-to-one function.

(a) If f(7) = 6,

 find f ⁻¹(6).

(b) If f ⁻¹(5) = −3,

 find f(−3).

Answer 1

f(7) = 6

f^-1(6) = 7

f^-1(5) =-3

f(-3) = 5

IF f(x) = y

then f^-1(y) = x

if (x,y) is a point on the graph of f(x)

then (y,x) is a point on the graph of the inverse function f^-1(x)

IF (6,7) is a point on f(x), then (7,6) is a point on f^-1(x)

if (5,-3) is a point on f^-1(x), then (-3,5) is on f(x)

draw a 45 degree diagonal line through the origin (0,0)

plot (6,7) which is above the line. (7,6) is an equal distance below the line

put a mirror along the diagonal line. the points above the line are reflected to the other side of the line

or rotate the graph about the diagonal line, by 180 degrees