Question

Let \[f=\left\{ x, \frac{x^2}{1+x^2}:x \in R \right\}\] be a function from R into R .Determine the range of f .

Answer 1

Take the limit as x approaches positive and negative infinities. Your answer for the range will be between the two limits.

Answer 2

wait ..soryy i didn't understand

Answer 3

You will see that there is a horizontal asymptote at a certain y = ? value. There is also a minimum value, so you will have to find that x value by setting the derivative equal to 0, and solving for the y-value that corresponds with the x value by plugging it into the equation. The range will be between the horizontal asymptote and the minimum value.