Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2019  MayJun  (P19709/12)  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 .
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