Question

F(x)= 1/x-2 g(x)= 4/x find (fog)(x)

Answer 1

We have the functions f and g:

f(x) = 1/x - 2

g(x) = 4/x

To obtain the composite function (f o g)(x):

(f o g)(x) = f(g(x)) = 1/g(x) - 2

Then:

(f o g)(x) = 1/(4/x) - 2

(f o g)(x) = x/4 - 2

Now, to calculate the composite function (g o f)(x):

(g o f)(x) = g(f(x)) = 4/f(x)

(g o f)(x) = 4/(1/x - 2) = 4/((1 - 2x)/x)

(g o f)(x) = 4x/(1 - 2x)