3. If f(x) = x -1 and g(x) = 1 / (𝑥+1) ,

Question

find the following functions i) f(g(x)) ii) g(f(1/2)

please solve both the parts , thank you.

Answer 1

i) f(g(x)) =

(1 / (x+1)) - 1

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

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

= -x / (x+1)

ii) g(f(1/2))

f(1/2) = (1/2) - 1 = -1/2

g(f(1/2)) = g(-1/2) = 1 / (-1/2 + 1) = 1 / (1/2) = 2