P={x: x is a factor of 6 } ⟹ P={1,2,3,6}P = \{ x : \;\text{x is a factor of 6}\; \} \implies P = \{1, 2, 3, 6\}P={x:x is a factor of 6}⟹P={1,2,3,6}
g(x)=x2+3x−5g(x) = x^{2} + 3x - 5g(x)=x2+3x−5
g(1)=12+3(1)−5=1+3−5=−1g(1) = 1^{2} + 3(1) - 5 = 1 + 3 - 5 = -1g(1)=12+3(1)−5=1+3−5=−1
g(2)=22+3(2)−5=4+6−5=5g(2) = 2^{2} + 3(2) - 5 = 4 + 6 - 5 = 5g(2)=22+3(2)−5=4+6−5=5
g(3)=32+3(3)−5=9+9−5=13g(3) = 3^{2} + 3(3) - 5 = 9 + 9 - 5 = 13g(3)=32+3(3)−5=9+9−5=13
g(6)=62+3(6)−5=36+18−5=49g(6) = 6^{2} + 3(6) - 5 = 36 + 18 - 5 = 49g(6)=62+3(6)−5=36+18−5=49
∴Range(g(x))={−1,5,13,49}\therefore \text{Range}(g(x)) = \{-1, 5, 13, 49\}∴Range(g(x))={−1,5,13,49}