I am a little short of time so will point you towards the solution of a similar problem: Q.1 (a) from last year:

The important thing to understand is how we use the properties of the absolute value function to simplify this and that we can only multiply both sides of an inequality by a positive thing… in this case after we write the absolute value of the fraction as a fraction of the absolute values, we multiply across by which is positive.

Regards,

J.P.

Could I just ask you for the answer of the Question one from last years test the inequality? The question is

.

Do I start this by multiplying both sides by the bottom thing squared?

]]>Algebraically we have the definition:

is increasing on if for all we have implies that .

Thinking like this we can say that if then at the very least as is the largest element of . Therefore if we have and increasing we have, by definition of increasing,

.

That is the technical answer.

Thinking geometrically helps though. If a function is increasing then the bigger the value of , the bigger the value of . In other words as grows from to the function is increasing so that it's maximum occurs at .

So the biggest can get on is and thus if you pick any we have

.

Regards,

J.P.

In one of the test solutions provided in the booklet it says:

Q: Suppose that is a function, increasing on the interval . Which of the following are true?

Ans: For any , .

Can you explain why this is the case ?

Thanks

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