Need a check on the following question [find f(g(x))]

[insideout]

Queston: If g(x)= (Square root (x+1)) and f(x)= x^2 + 2, find f[g(x)].

My solution:
P[g(x)] = f[sqaure root (x + 1)]
. . . .. . .= (square root x^2 + 1)^2 + 2
. . . .. . .= (x^2 + 1) + 2
. . . .. . .= (x^2 +3)

Please help me if this is not the right answer..thanks.

 

[stapel]

How does P(x) relate to f(x) and g(x)?

Thank you.

Eliz.

 

[tkhunny]

What about if it IS the right answer? The big "P" should be an "f", right?

Sorry I confused you on your previous visit.

You have it. I am glad to see thatyour 'x' stayed an 'x' this time.

 

[daon]

Queston: If g(x)= (Square root (x+1)) and f(x)= x^2 + 2, find f[g(x)].

My solution:
P[g(x)] = f[sqaure root (x + 1)]
. . . .. . .= (square root x^2 + 1)^2 + 2
. . . .. . .= (x^2 + 1) + 2
. . . .. . .= (x^2 +3)

Please help me if this is not the right answer..thanks.

If P means "f" then you have a mistake.
You have: f(sqrt(x+1)) = (sqrt(x^2+1))^2 + 2
But it should be: f(sqrt(x+1)) = (sqrt(x+1))^2 + 2

There should be no square in your final answer.