What is the domain of f(x)=(3x-1)/(sqrt(-x^2+x+20)) ?

The domain of f(x)=(3x-1)/(sqrt(-x^2+x+20)) is -4<x<5

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domain of f(x)=(3x-1)/(sqrt(-x^2+x+20))

domain

f (x) = \frac{3 x - 1}{- x ^{2} + x + 20}

- 4 < x < 5

Interval Notation

(- 4, 5)

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 5

Find undefined (singularity) points:

x = - 4, x = 5

Combine real regions and undefined points for final function domain

- 4 < x < 5

What is the domain of f(x)=(3x-1)/(sqrt(-x^2+x+20)) ?
The domain of f(x)=(3x-1)/(sqrt(-x^2+x+20)) is -4<x<5