Theory question 103
FunctionsA function f is defined by f(x) = 72/(px + r), where p and r are constants. Given that f(6) = 12 and f(7) = 9, find: (a) the values of p and r. (b) f−1(5/3)
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Model answer
(a) 72/(6p + r) = 12 gives 6p + r = 6; 72/(7p + r) = 9 gives 7p + r = 8.
Subtracting: p = 2, then r = −6.
(b) f(x) = 72/(2x − 6). f⁻¹(5/3) is the x with 72/(2x − 6) = 5/3:
2x − 6 = 216/5, 2x = 246/5, x = 123/5 (= 24.6).
Explanation
f⁻¹(k) is the input that gives output k.