find the domain of the following function f(x)=x/x2+3x+2

1.	find the domain of the following function f(x)=x/x2+3x+2
Answer» f(x) = x/x^2 + 3x + 2 x^2 + 3x + 2 = 0x^2 + 2x + x + 2 = 0x(x + 2) + 1(x + 2) = 0(x + 1)(x + 2) = 0x = - 1, - 2 This means that, whenx=−1or- 2, we have thex^2 + 3x + 2 = 0Implying thatf(x) = x/0which isundefined. Hence, the domain is all real numbers except−1 and- 2 Also written asDf=(−∞,−2)∪(-1,+∞)

Answer»

f(x) = x/x^2 + 3x + 2

x^2 + 3x + 2 = 0x^2 + 2x + x + 2 = 0x(x + 2) + 1(x + 2) = 0(x + 1)(x + 2) = 0x = - 1, - 2

This means that, whenx=−1or- 2, we have thex^2 + 3x + 2 = 0Implying thatf(x) = x/0which isundefined.

Hence, the domain is all real numbers except−1 and- 2

Also written asDf=(−∞,−2)∪(-1,+∞)

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