Composition of Functions (check me)

12
0
Hi,

1. The problem statement, all variables and given/known data
Given:[tex] f(x)=x^2+2[/tex] and [tex] g (x)=\sqrt{x}[/tex]

Find: [tex] f \circ g [/tex] and [tex] g \circ f [/tex]

2. The attempt at a solution
[tex] f \circ g =f(g(x))=x+2 [/tex], where [tex] x\in (-\infty ; +\infty) [/tex]

[tex] g \circ f =g(f(x))=\sqrt{x^2+2} [/tex] where [tex] x\in (-\infty ;+ \infty) [/tex]

I haven't done this for a while, and I'm not sure about my solution. Is it correct?
 

Dick

Science Advisor
Homework Helper
26,249
611
Almost. Except g(x) is only defined for x in [0,infinity).
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top