Find the domains of f gx and g fx fx x2 10 gx 1x 1 Selec

Find the domains of (f g)(x) and (g f)(x). f(x) = x^2 - 10; g(x) = 1/x + 1 Select the correct choice below and, if necessary fill in the answer box within your choice. A. The domain of (f g) is. B. The domain is all real numbers Select the correct choice below and if necessary fill in the answer box within your choice. A. The domain of (g f)(x) is. B. The domain is all real numbers.

Solution

f(x) = x^2 -10 ; g(x) = 1/(x+1)

(f o g)(x) = f(g(x)) = 1/(x+1)^2 - 10

( go f)(x) = g(f(x) = 1/(x^2 -10 +1) = 1/(x^2 -9)

Domain of ( f o g)(x) : xshould not be equal to -1

(- inf, -1) U (-1 , inf)

Domain of (g o f )(x) = x should not be equal to +/- 3

So, Domain : (-inf , -3) U ( -3, 3) U ( 3, inf)