1 of 8 0-day streak

Find the maximal domain of an algebraic function

Question 1 of 8

No calculator

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

h(u)=\frac{1}{3\left(u+\frac{1}{4}\right)}

(a)1 mark

What domain restriction is contributed by the denominator \(3\left(u+\frac{1}{4}\right)\)?

u\in\left(-\infty,\;-\frac{1}{4}\right)\;\cup\;\left(-\frac{1}{4},\;\infty\right)

u\in\left(-\infty,\;\frac{3}{4}\right)\;\cup\;\left(\frac{3}{4},\;\infty\right)

u\in\mathbb{R}

(b)1 mark

Which statement gives the natural domain of h?

u\in\left(-\infty,\;-\frac{1}{4}\right)\;\cup\;\left(-\frac{1}{4},\;\frac{3}{4}\right)\;\cup\;\left(\frac{3}{4},\;\infty\right)

u\in\left(-\infty,\;\frac{3}{4}\right)\;\cup\;\left(\frac{3}{4},\;\infty\right)

u\in\left(-\infty,\;-\frac{1}{4}\right)\;\cup\;\left(-\frac{1}{4},\;\infty\right)

u\in\mathbb{R}