What is the domain of f(t)= t/(sqrt(4-t)-2) ?

The domain of f(t)= t/(sqrt(4-t)-2) is t<0\lor 0<t<= 4

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domain of f(t)= t/(sqrt(4-t)-2)

domain

f (t) = \frac{t}{4 - t - 2}

t < 0 or 0 < t \leq 4

Interval Notation

(- \infty, 0) \cup (0, 4]

Solution steps

Find non-negative values for radicals:

t \leq 4

Find undefined (singularity) points:

t = 0

Combine real regions and undefined points for final function domain

t < 0 or 0 < t \leq 4

x - 4

x + 2 y = - 3

(3.2) (- 8.4)

\frac{6 - 3 x}{x ^{2} - 5 x + 6}

\frac{x}{1 + x}

What is the domain of f(t)= t/(sqrt(4-t)-2) ?
The domain of f(t)= t/(sqrt(4-t)-2) is t<0\lor 0<t<= 4