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

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

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

domain

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

x < - 3 or - 3 < x \leq 1

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x \leq 1

\frac{4 x + 3}{x ^{2} - 1}

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

9^{x} x^{22 x} (x^{2} + 2 x)^{2}

\frac{x ^{2}}{7 - x}

f (x) = \frac{1}{4} x^{2} - 5 x + 11

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