Question

f(x)= (x^2 + 1)^2
g(x)= (1)/(sqrt(x+5))

what is f of g
what is g of f

please show work for both
thanks in advance

Answer 1

(fog)= ( (1/sqrt.x+5)^2 +1)^2 = (x^2 +12x +36) / (x^2 +10x+ 25)
I just inserted g(x) into x of f(x)
(gof)= 1/(sqrt.((x^2 +1)^2 ) +5)

Answer 2

for the second one, just multiply the numerator and deonominator by the conjugate of the squareroot