Posted by John on Sunday, September 12, 2010 at 6:28pm.
I assume you mean
f(x)=20/(1+x²)
Parentheses are important when posting mathematical formulas because with multiplication/division taking precedence over addition and subtraction, the posted function would not be very meaningful.
The domain of a function means the values that x can take up, which in this case, is ℝ (= all real numbers).
The range of a function is the range of values f(x) can take up for any possible values of x.
In this case, the maximum is when x=0, which gives f(0)=20.
The minimum is lim x->∞ f(x)=0.
Therefore the range of the given function is
]0,20], or altrenatively, (0,20] in interval notation.