Functions

Step 1: Range of .
The sine function oscillates between -1 and 1 for all real values of . Hence, the range of is:
Step 2: Range of .
The function is a parabola that opens upwards, with a minimum value of 0 when . Since for all , the range of is:
Step 3: Conclusion.
The range of is and the range of is .

Step 1: Find
Step 2: Find
Step 3: Compare and
Step 4: Show they are not equal by counterexample Take : Since , we have .
Step 5: Conclusion Since for at least one value of (here ), the two composite functions are not equal. Therefore: