This part of the question is just testing your knowledge of inequalities. You have worked out the points of intersection between f(x) and g(x) in part i. All you need to do is recognise that the value of f(x) (in other words, the y-value, for a given value of x) is greater than g(x) when x > 4 or x < -3. You can figure this out in the exam by quickly sketching each function and looking at where the value of y, for a given value of x, for f(x) is greater than g(x). In layman's terms, this is when the line is 'above' the curve. An alternative method, (although I wouldn't recommend this as you will be doing more work than necessary) is manipulating the algebra so that you are solving a quadratic inequality by itself. You will to still have to sketch the quadratic and find the relevant solutions, however. I have included an image below to help you visualise both methods. Let me know if you need more help. I would recommend practising more inequality questions as they can become even trickier (such as with modulus functions!).
This part of the question is just testing your knowledge of inequalities. You have worked out the points of intersection between f(x) and g(x) in part i. All you need to do is recognise that the value of f(x) (in other words, the y-value, for a given value of x) is greater than g(x) when x > 4 or x < -3. You can figure this out in the exam by quickly sketching each function and looking at where the value of y, for a given value of x, for f(x) is greater than g(x). In layman's terms, this is when the line is 'above' the curve. An alternative method, (although I wouldn't recommend this as you will be doing more work than necessary) is manipulating the algebra so that you are solving a quadratic inequality by itself. You will to still have to sketch the quadratic and find the relevant solutions, however. I have included an image below to help you visualise both methods. Let me know if you need more help. I would recommend practising more inequality questions as they can become even trickier (such as with modulus functions!).
Thanks for all your questions man! We’ll get to answering them over the next couple days. Hope that’s ok :)