find ( f o g)(x) and ( f o g)(-3) of the functions f(x) = x^2 +1/ x^2 -2 and sqroot of x-1

Question

Somebody please help with these problems !

Answer 1

find ( f o g)(x) and ( f o g)(-3) of the functions f(x) = x^2 +1/ x^2 -2 and g(x) = sqroot of x-1.

f(x) = (x^2 + 1)/(x^2 - 2)

g(x) = sqrt(x - 1)

( f o g)(x) = f(g(x)) = f(sqrt(x-1)) = ((sqrt(x - 1))^2 + 1)/((sqrt(x - 1))^2 - 2)

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

( f o g)(x) = x/(x-3)

( f o g)(-3) = (-3)/(-3 - 3) = -3/-6 = 1/2

( f o g)(-3) = 1/2