What is the domain of f(x)=(sqrt(t-4))/(3t-21) ?

The domain of f(x)=(sqrt(t-4))/(3t-21) is 4 7

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domain of f(x)=(sqrt(t-4))/(3t-21)

domain

f (x) = \frac{t - 4}{3 t - 21}

4 \leq t < 7 or t > 7

Interval Notation

[4, 7) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

t \geq 4

Find undefined (singularity) points:

t = 7

Combine real regions and undefined points for final function domain

4 \leq t < 7 or t > 7

\frac{x ^{2}}{x ^{2} + 1}

f (x) = - 2 x + 5

f (x) = x^{2} + 6 x + 4

\frac{x}{x ^{2} - 6 x + 8}

f (x) = - x + 5 - 3

What is the domain of f(x)=(sqrt(t-4))/(3t-21) ?
The domain of f(x)=(sqrt(t-4))/(3t-21) is 4<= t<7\lor t>7