What is the domain of f(x)=sqrt(1-t)+1/(t+3)+t^2+2 ?

The domain of f(x)=sqrt(1-t)+1/(t+3)+t^2+2 is t<-3\lor-3<t<= 1

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domain of f(x)=sqrt(1-t)+1/(t+3)+t^2+2

domain

f (x) = 1 - t + \frac{1}{t + 3} + t^{2} + 2

t < - 3 or - 3 < t \leq 1

Interval Notation

(- \infty, - 3) \cup (- 3, 1]

Solution steps

Find non-negative values for radicals:

t \leq 1

Find undefined (singularity) points:

t = - 3

Combine real regions and undefined points for final function domain

t < - 3 or - 3 < t \leq 1

\frac{1}{4} x

y = x^{2} + 1

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

y = x^{2} - 1

What is the domain of f(x)=sqrt(1-t)+1/(t+3)+t^2+2 ?
The domain of f(x)=sqrt(1-t)+1/(t+3)+t^2+2 is t<-3\lor-3<t<= 1