(i) Solve the inequality, leaving your answers in exact form, (ii) Hence solve

Given that a is a positive real number, solve the inequality leaving your answer in terms of a.

The functions f and g are defined as follows: Where λ is a constant. (i) Given that gf exists, find the largest value of λ. In the rest of the questions, use the value of λ found in part (i). (ii) On the same diagram, sketch the graph of , and , showing clearly the relationship between the graphs. […]

Two functions f and g are defined as follows: Determine, with reasons, whether fg and gf exist. If the composite function exists, give the rule, domain and range in exact form.

The binomial expansion of , where n is a positive integer, in ascending power of x, is . Find the value of n and of k.

In the expansion of in the ascending power of , the coefficient of the third term is 121. Find the value of n.

Find, in ascending powers of x, the first four terms in the expansion of . Things to note: Expansion by binomial theorem is all about pattern recognition. Note that the numbers in light blue are in ascending or descending down the expansion.

Given that the equation has a root of 1-2i, solve the equation.

(i) Sketch the curve for (ii) Find the -coordinates of the points of intersection of the curve and the line y=27.

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