Q. 135.0( 3 Votes )

If f : R R be defined by f(x) = x2 + 1, then find f-1{17} and f-1{–3}.

Answer :

Given f : R R and f(x) = x2 + 1.


We need to find f-1{17} and f-1{–3}.


Let f-1{17} = x


f(x) = 17


x2 + 1 = 17


x2 – 16 = 0


(x – 4)(x + 4) = 0


x = ±4


Clearly, both –4 and 4 are elements of the domain R.


Thus, f-1{17} = {–4, 4}


Now, let f-1{–3} = x


f(x) = –3


x2 + 1 = –3


x2 = –4


However, the domain of f is R and for every real number x, the value of x2 is non-negative.


Hence, there exists no real x for which x2 = –4.


Thus, f-1{–3} =


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