Consider the following functions: f(x) = x/x+7, g(x) = 2x-7. Find (f o f)(x) and the domain of (f o f)(x).

Question

Consider the following functions: f(x) = x/x+7, g(x) = 2x-7.

Find (f o f)(x) and the domain of (f o f)(x) using interval notation.

Thank you for your help!

Answer 1

We start by defining

f(y)=y/(y+7)

and now instead of y we use f(x)=x/(x+7). Therefore, anytime we see y we replace it with x/(x+7)

f(y)=f(f(x))=(x/(x+7)) / (x/(x+7) +7) which can be rewritten as x/(x+7) * (x+7)/(x+7x+49) = x/(8x+49)

The domain of this new function are all real numbers apart from x=-49/8 for which the denominator of the above function becomes zero.

Best,

Davide