Homework SourseFind the f o g and the g o f when Fx 2x 1 Gx x2 1 Then det
Find the f o g and the g o f when
F(x)= 2x + 1
G(x)= x^2 - 1
Then determine the domains for both f o g and g o f
Find the f o g and the g o f when
F(x)= 2x + 1
G(x)= x^2 - 1
Then determine the domains for both f o g and g o f
F(x)= 2x + 1
G(x)= x^2 - 1
Then determine the domains for both f o g and g o f
Solution
f(x) = 2x +1 ; g(x) = sqrt( x^2 -1)
To find (f o g)(x) plug x = g(x) in f(x)
(f o g)(x) = 2sqrt( x^2 -1) +1
Domain: x^2 -1 >=0
( - inf , +inf)
To find ( g o f)(x) plug x = f(x)
(g o f)(x) = sqrt( (2x+1)^2 -1)
= sqrt( 4x^2 +4x +1 -1)
= sqrt( 4x^2 +4x)
2sqrt(x^2 +x)
Domain: ( -inf , inf)
