What is the domain of f(x)= 1/(sqrt(4x^2-17x+4)) ?

The domain of f(x)= 1/(sqrt(4x^2-17x+4)) is x 4

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domain of f(x)= 1/(sqrt(4x^2-17x+4))

domain

f (x) = \frac{1}{4 x ^{2} - 17 x + 4}

x < \frac{1}{4} or x > 4

Interval Notation

(- \infty, \frac{1}{4}) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq \frac{1}{4} or x \geq 4

Find undefined (singularity) points:

x = 4, x = \frac{1}{4}

Combine real regions and undefined points for final function domain

x < \frac{1}{4} or x > 4

\frac{( 2 x - 1 )}{2 x + 5}

f (x) = - x^{4}

f (x) = \frac{( x - 9 )}{( x + 9 )}

2 x - y = 5

f (x) = \frac{x + 1}{x ^{2} - 4 x - 12}

What is the domain of f(x)= 1/(sqrt(4x^2-17x+4)) ?
The domain of f(x)= 1/(sqrt(4x^2-17x+4)) is x< 1/4 \lor x>4