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

This composition of functions requires you to plug the g(x) function into every place that the f(x) function has an x. Just keep an eye on which function you are working with first. It is similar to programming as well, if that helps. You solve the inner function first.

It is:

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

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

g(f(1/2)) = 1 / (0.5 -1) + 1 = 1 / (-0.5) + 1

= - 1/(1/2) + 1

= -2 + 1

= -1

another way is to finish the f(1/2) first

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

then plugin

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