Adding f(x) and g(x): Domain and Output

[Caldus]

If f(x) = square root of x and g(x) = x + 1, then:

1. What is f+g(x)?
2. Domain of f+g(x)?
3. What is f(g(x))?
4. What is the domain of f(g(x))?

I put:

1. square root of x + x + 1
2. x >= 0
3. square root of x + 1
4. All real numbers?

Thanks.

 

[Muzza]

Number 4 depends on whether you "allow" complex numbers or not...

 

[ahrkron]

Originally posted by Caldus
1. square root of x + x + 1

Just to make sure, do you mean
sqrt(x) + x+1
or
sqrt(x+x+1)
??

2. x >= 0

OK (as long as you are only talking about reals)

3. square root of x + 1

Again, use parentheses.

4. All real numbers?

Nope. Example: x = -3.

 

[HallsofIvy]

In #2 you had already asserted that the domain of g+h (x)= √(x)+ x+1 is x>= 0 so you are talking about real valued functions of a real value (you can't take the square root of a negative number).

In #4, then, f(g(x))= &radic(x+1), you must have x+1>= 0.

 

[Caldus]

Ug I hate it when I make mistakes like this! I knew how to do it and then when I'm under pressure I mess up everytime! Ack. So frustrating...lol... Oh well, just a quiz grade. Maybe I can make it up somehow...lol...