Functions

Step 1: As , the argument of also tends to . For small ,
Step 2: Hence,
Step 3: Divide both sides by ( ):
Step 4: Taking the limit :
Step 5: Therefore,

Step 1: Rewrite the function:
Step 2: Check one–one property The derivative of is: Since is always positive, is strictly increasing. Hence, is one–one.
Step 3: Check onto property For all real , [ -1]
Step 4: Since the codomain is but the range is only , the function does not cover all real numbers. Hence, is into but not onto.