What is the domain of f(x)= 1/(4-sqrt(1-x)) ?

The domain of f(x)= 1/(4-sqrt(1-x)) is x<-15\lor-15<x<= 1

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domain of f(x)= 1/(4-sqrt(1-x))

domain

f (x) = \frac{1}{4 - 1 - x}

x < - 15 or - 15 < x \leq 1

Interval Notation

(- \infty, - 15) \cup (- 15, 1]

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = - 15

Combine real regions and undefined points for final function domain

x < - 15 or - 15 < x \leq 1

f (x) = \frac{x ^{2} + 6 x - 27}{x + 9}

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

\frac{4}{x ^{2} - 5 x + 6}

2 T - 3

What is the domain of f(x)= 1/(4-sqrt(1-x)) ?
The domain of f(x)= 1/(4-sqrt(1-x)) is x<-15\lor-15<x<= 1