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}{3\left(x-\frac{3}{2}\right)}

(a)1 mark

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

x\in\mathbb{R}

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

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

(b)1 mark

Which statement gives the natural domain of f?

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

x\in\mathbb{R}

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

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