checking my answer......

[OTHfan]

Find f[g(x)] and g[f(x)].

f(x) =

; g(x) = 4x - 1

f[g(x)] =

g[f(x)] =

 

[Gene]

Close but f(a) REPLACES the x with a.
f(g(x)) = f(4x-1) =
sqrt((4x-1)+5)
Try the second again.

 

[OTHfan]

f(g(x)) = sqrt 4x^2 + 1

g(f(x)) = sqrt 4x^2 - 5

 

[Gene]

Look at my post again. Where are you getting an x² term???

 

[OTHfan]

f(g(x)) = 2 sqrt x + 5

g(f(x)) = 4 sqrt x + 1 - 1

 

[Gene]

Well, you are sneaking up on it. When you simplify you should get
sqrt((4x-1)+5) =
sqrt(4x+4) =
2sqrt(x+1)

g(f(x)) = g(sqrt(x+5))
Show your steps from there, not just your answer.