1 of 8 0-day streak

Find the maximal domain of an algebraic function

Question 1 of 8

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Let \(f(x)\) be the function defined by

f(x)=\frac{1}{-2\left(x+\frac{5}{3}\right)}

(a)1 mark

What domain restriction is contributed by the denominator \(-2\left(x+\frac{5}{3}\right)\)?

x\in\left(-\infty,\;-\frac{5}{3}\right)\;\cup\;\left(-\frac{5}{3},\;\infty\right)

x\in\left(-\infty,\;-\frac{2}{3}\right)\;\cup\;\left(-\frac{2}{3},\;\infty\right)

x\in\mathbb{R}

(b)1 mark

Select the maximal real domain of f

x\in\left(-\infty,\;-\frac{5}{3}\right)\;\cup\;\left(-\frac{5}{3},\;\infty\right)

x\in\mathbb{R}

x\in\left(-\infty,\;-\frac{5}{3}\right)\;\cup\;\left(-\frac{5}{3},\;-\frac{2}{3}\right)\;\cup\;\left(-\frac{2}{3},\;\infty\right)

x\in\left(-\infty,\;-\frac{2}{3}\right)\;\cup\;\left(-\frac{2}{3},\;\infty\right)