What is the domain of f(x)=(sqrt(x^2-25))/(3x-24) ?

The domain of f(x)=(sqrt(x^2-25))/(3x-24) is x 8

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domain of f(x)=(sqrt(x^2-25))/(3x-24)

domain

f (x) = \frac{x ^{2} - 25}{3 x - 24}

x \leq - 5 or 5 \leq x < 8 or x > 8

Interval Notation

(- \infty, - 5] \cup [5, 8) \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 5

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

x \leq - 5 or 5 \leq x < 8 or x > 8

f (x) = \frac{3 x}{x ^{2} - 7 x + 12}

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

y = \frac{x ^{2} - 25}{lo g _{5} ( x ^{2} + 4 x + 4 )}

f (x) = \frac{( x - 6 )}{x ^{2} - 1}

f (x) = \frac{x ^{2} - 6}{x ^{2} - 1}

What is the domain of f(x)=(sqrt(x^2-25))/(3x-24) ?
The domain of f(x)=(sqrt(x^2-25))/(3x-24) is x<=-5\lor 5<= x<8\lor x>8