What is the domain of f(x)=(x-4)/(sqrt(25-x^2)) ?

The domain of f(x)=(x-4)/(sqrt(25-x^2)) is -5<x<5

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domain of f(x)=(x-4)/(sqrt(25-x^2))

domain

f (x) = \frac{x - 4}{25 - x ^{2}}

- 5 < x < 5

Interval Notation

(- 5, 5)

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 5

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

- 5 < x < 5

What is the domain of f(x)=(x-4)/(sqrt(25-x^2)) ?
The domain of f(x)=(x-4)/(sqrt(25-x^2)) is -5<x<5