What is the domain of f(x)=sqrt(25-(x+7)^2),x<=-2 ?

The domain of f(x)=sqrt(25-(x+7)^2),x<=-2 is -12<= x<=-2

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domain of f(x)=sqrt(25-(x+7)^2),x<=-2

domain

f (x) = 25 - (x + 7)^{2}, x \leq - 2

- 12 \leq x \leq - 2

Interval Notation

[- 12, - 2]

Solution steps

Set the domain to the given interval

x \leq - 2

Find non-negative values for radicals:

- 12 \leq x \leq - 2

Join real regions with the domain:

- 12 \leq x \leq - 2 and x \leq - 2

- 12 \leq x \leq - 2

\frac{3 x - 8}{7 - x}

f (x) = \frac{x ( x + 1 ) ( x - 6 )}{x + 8}

f (x) = \frac{x}{2 x - 5}

\frac{5 x - 4}{( x - 7 ) ^{2}}

f (x) = \frac{6 x ^{2} + 7}{8 x + 6}

What is the domain of f(x)=sqrt(25-(x+7)^2),x<=-2 ?
The domain of f(x)=sqrt(25-(x+7)^2),x<=-2 is -12<= x<=-2