f(x) = - 4x - 2 and g(x) = sqrt x - 1. Determine each of the following. (please show me step by step.)

Question

f ° g (x)

g ° f(x)

Answer 1

oh no, is g(x)= (sqrt(x))-1

or is it g(x) = sqrt (x-1)

in other words, is the 1 under the square root or not?

The problem now has to be done TWICE!!!

g(x) = sqrt(x) -1 <-- 1 is NOT under the square root

f(g(x)) = -4 [ sqrt(x) - 1] - 2

= -4 * sqrt(x) + 4 - 2

= -4 * sqrt(x) + 2

domain x>=0

g(f(x)) = sqrt( -4x-2) - 1;

domain: -4x-2>=0

-4x >= 2

x <= -1/2

==========================================

g(x) = sqrt( x-1) <-- 1 IS under the square root

f(g(x)) = -4 [ sqrt(x-1)] - 2

domain x-1>=0 --->x >= 1

g(f(x)) = sqrt( -4x-2-1) = sqrt(-4x-3)

domain -4x-3>=0 ---> -4x >=3 ---> x <= -3/4