Examples
f(x)=√xf(x)=√x , g(x)=x+1g(x)=x+1 , f(g(x))f(g(x))
Step 1
Set up the composite result function.
f(g(x))f(g(x))
Step 2
Evaluate f(x+1)f(x+1) by substituting in the value of gg into ff.
f(x+1)=√x+1f(x+1)=√x+1
Step 3
Remove parentheses.
√x+1√x+1
Step 4
Set the radicand in √x+1√x+1 greater than or equal to 00 to find where the expression is defined.
x+1≥0x+1≥0
Step 5
Subtract 11 from both sides of the inequality.
x≥-1x≥−1
Step 6
The domain is all values of xx that make the expression defined.
Interval Notation:
[-1,∞)[−1,∞)
Set-Builder Notation:
{x|x≥-1}{x|x≥−1}
Step 7
