What is the domain of f(x)=(sqrt(-5x+3))/(x^2-3x-40) ?

The domain of f(x)=(sqrt(-5x+3))/(x^2-3x-40) is x<-5\lor-5<x<= 3/5

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domain of f(x)=(sqrt(-5x+3))/(x^2-3x-40)

domain

f (x) = \frac{- 5 x + 3}{x ^{2} - 3 x - 40}

x < - 5 or - 5 < x \leq \frac{3}{5}

Interval Notation

(- \infty, - 5) \cup (- 5, \frac{3}{5}]

Solution steps

Find non-negative values for radicals:

x \leq \frac{3}{5}

Find undefined (singularity) points:

x = 8, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or - 5 < x \leq \frac{3}{5}

f (x) = 10 x^{2} + 9 x + 100

y = \frac{- 7}{( x - 2 ) ^{2}}

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

\frac{2 x - 1}{x ^{2} + x - 12}

f (x) = - 2 (x - 1)^{2} + 5 = 0

What is the domain of f(x)=(sqrt(-5x+3))/(x^2-3x-40) ?
The domain of f(x)=(sqrt(-5x+3))/(x^2-3x-40) is x<-5\lor-5<x<= 3/5