What is the domain of f(x)=sqrt((6x)/(x^2-14x+45)) ?

The domain of f(x)=sqrt((6x)/(x^2-14x+45)) is 0 9

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domain of f(x)=sqrt((6x)/(x^2-14x+45))

domain

f (x) = \frac{6 x}{x ^{2} - 14 x + 45}

0 \leq x < 5 or x > 9

Interval Notation

[0, 5) \cup (9, \infty)

Solution steps

Find non-negative values for radicals:

0 \leq x < 5 or x > 9

Find undefined (singularity) points:

x = 9, x = 5

Combine real regions and undefined points for final function domain

0 \leq x < 5 or x > 9

(x - 9) (x^{2} - 18 x - 162)

2 x^{2} + 5 x - 12

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

f (x) = lo g_{10} (\frac{x - 3}{2})

(x^{2} + x)^{2} + (x^{2} + x)

What is the domain of f(x)=sqrt((6x)/(x^2-14x+45)) ?
The domain of f(x)=sqrt((6x)/(x^2-14x+45)) is 0<= x<5\lor x>9