Let f: RR be given by f(x) = x² + 3 Find
(i) {x : f(x) = 28}
(ii) The pre-images of 39 and 2 under ‘f’.

posted in: | updated on: 15 Jun, 2012

(i) Given f(x) = 28 = x² + 3
        x² = 28 – 3 = 25
x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»25«/mn»«/msqrt»«/math» = 5
(ii)  To find f^-1 (39) and f^-1 (2)
f^-1 (39) = x  f (x) = 39 = x² + 3
x² = 39 – 3 = 36
x = = 6
f^-1 (2) = x f (x) = 2 = x² + 3
x² = 2 – 3 = -1
x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msqrt»«/math» .