What is the domain of P(t)=(sqrt(t-5))/(3t-24) ?

The domain of P(t)=(sqrt(t-5))/(3t-24) is 5 8

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domain of P(t)=(sqrt(t-5))/(3t-24)

domain

P (t) = \frac{t - 5}{3 t - 24}

5 \leq t < 8 or t > 8

Interval Notation

[5, 8) \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

t \geq 5

Find undefined (singularity) points:

t = 8

Combine real regions and undefined points for final function domain

5 \leq t < 8 or t > 8

f (x) = \frac{1}{2} (x + 1)^{2} - 12

f (x) = \frac{5 x}{∣ x ∣ - 2}

f (x) = 120 x - 3 x^{2}

f (x) = 2^{3} x

(x - 10) (x + 2)

What is the domain of P(t)=(sqrt(t-5))/(3t-24) ?
The domain of P(t)=(sqrt(t-5))/(3t-24) is 5<= t<8\lor t>8