If f(x) = 2x - 1, g(x) = (x + 1)/2, show that fog = gof = x.

Solution:

f(x) = 2x -1

g(x) = (x + 1)/2

To calculate fog x,

f(x) is replaced by g(x)

i.e. (x+1)/2 as shown below:

fog = 2[(x+1)/2] - 1 = x + 1 - 1 = x

To calculate gof,

g(x) is replaced by f(x)

i.e. 2x - 1 as shown below:

gof = (2x -1 + 1)/2 = 2x/2 = x

Hence fog = gof = x

If f(x) = 2x - 1, g(x) = (x + 1)/2, show that fog = gof = x.

Summary:

When f(x) = 2x - 1, g(x) = (x + 1)/2, then fog = gof = x