If A={x:|x|≤5;x∈Z−{0}}, B={x:x≤100;x∈W} and f:A→B is a function defined by f(x)=x2+1, then the number of elements in the range of f that lie in [5,26) is
A
5
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B
3
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C
4
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D
2
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Solution
The correct option is B3 A={−5,−4,−3,−2,−1,1,2,3,4,5}B={0,1,2,⋯,100} f(x)=x2+1 f(−5)=f(5)=25+1=26f(−4)=f(4)=16+1=17f(−3)=f(3)=9+1=10f(−2)=f(2)=4+1=5f(−1)=f(1)=1+1=2
∴R(f)={2,5,10,17,26}
Hence, the required number of elements in R(f) that lie in [5,26) is 3 i.e {5,10,17}