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Find the maximal domain of an algebraic function

Question 1 of 8

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Let \(h(u)\) be the function defined by

h(u)=\frac{1}{-2\left(u-\frac{5}{3}\right)}

(a)1 mark

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

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

u\in\mathbb{R}

u\in\left(-\infty,\;\frac{8}{3}\right)\;\cup\;\left(\frac{8}{3},\;\infty\right)

(b)1 mark

Which statement gives the natural domain of h?

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

u\in\left(-\infty,\;\frac{8}{3}\right)\;\cup\;\left(\frac{8}{3},\;\infty\right)

u\in\mathbb{R}

u\in\left(-\infty,\;\frac{5}{3}\right)\;\cup\;\left(\frac{5}{3},\;\frac{8}{3}\right)\;\cup\;\left(\frac{8}{3},\;\infty\right)