Consider the functions fx 2x 3 and gx Squareroot x 1 Fin

Consider the functions: f(x) = 2x - 3 and g(x) = Squareroot x + 1 Find (g o f)(x). Be sure to simplify your final answer completely. Find the domain of the above composite function. Be sure to state your final answer using interval notation.

Solution

f(x) = 2x -3 ; g(x) = sqrt(x+1)

a) ( g o f)(x) :

plug x = f(x) in g(x)

( g o f)(x) = sqrt[ 2x -3 +1] = sqrt( 2x -2)

Domain : 2x -2 >=0

x >=1

[1, inf )