WAEC Further Mathematics 2023 Objective — Question 10

Question 10 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2023 Objective paper, with the correct answer and a full explanation.

If f(x) = (2-x)/x, x not 0, find the inverse of f.

A. 2/(x-1), x != 1
B. 2/(x+1), x != -1Correct
C. 2/(1-x), x != 1
D. x/(2+x), x != -2

Explanation

Let y=(2-x)/x => xy=2-x => xy+x=2 => x(y+1)=2 => x=2/(y+1). So f^-1(y)=2/(y+1), y != -1, i.e. f^-1(x)=2/(x+1), x != -1.

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