Question

Determine the domain of the given function f(t)=(t+2)/sqrt(9-t^2)

Answer 1

Gven function f(t) = (t+2)/sqrt(9-t^2)

First set the denominator greater than  to 0.

9-t^2 > 0

(3+t)(3-t) > 0

3+t > 0

Subtract 3 from each side.

3+t-3 > 0-3

t > -3

and 3-t > 0

Subtract 3 from each side

and 3-3-t > 0-3

-t > -3

Multiple to each side by negitive 1 and change the inequality symbol.

t < 3

So -3 to 3 must be omitted from the domain.

Next find the domian of numarator equal to 0.

t+2 = 0

t = -2

Combining the two results gives the domain for entire function.

Domain is the set of all real numbers t for which -3< t < 3.