# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#7

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Question

The functions f and g are defined by ,  , i.Obtain expressions for and , stating the value of x for which is not defined.

ii.Solve the equation Solution

i.

We are given; for  for We have;  We write them as;  To find the inverse of a given function we need to write it in terms of rather than in  terms of .       Interchanging ‘x’ with ‘y’;    We are also required to find the domain of .

The set of numbers for which function is defined is called domain of the function.

Finding domain of a function :

·Since denominator of a fraction cannot be zero, equate denominator of function with zero  and solve for set of values of which produce zero in the denominator. Exclude these values of from domain of ·Since the number under square root must be positive , make the inequality of number under  square root with and solve for set of values of which produce negative number under square  root. Exclude these values of from domain of Therefore, is defined for all except .

ii.

We are given; for  for We can write it as;  We are required to solve the equation .         