Question

Given the functions f(x) = 2x-7/x+1 and g(x) =2√x find:
A) (f º g)(x) and state domain
B) (g º f)(x) and state domain
C) (f º g) (9)

Answer 1

to find (fog)(x)= just substitute the value of g(x) at x in f(x) and in (gof) use value of f(x) in g(x)...

Answer 2

As @ghazi says:
\[(f \ o\ g)(x) = \frac{4\sqrt{x}-7}{\sqrt{x}+1}\]
\[(g\ o\ f)(x) = 2\sqrt {\frac{2x -7}{x+1}}\]
Domain for the first is not restricted since sqrt(x) >= 0 for all x.
Domain for the second: x cannot be equal to -1.
Compute (f o g)(9) = (12-7)/(3 + 1) = 5/4

Answer 3

Oh, and additional restriction for the second (2x - 7) >= 0 only.

Answer 4

Oh, and additional restriction for the first: x >= 0.