What is the domain of (sqrt(X+4))/(-4X+3) ?

The domain of (sqrt(X+4))/(-4X+3) is -4 3/4

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domain of (sqrt(X+4))/(-4X+3)

domain

\frac{X + 4}{- 4 X + 3}

- 4 \leq X < \frac{3}{4} or X > \frac{3}{4}

Interval Notation

[- 4, \frac{3}{4}) \cup (\frac{3}{4}, \infty)

Solution steps

Find non-negative values for radicals:

X \geq - 4

Find undefined (singularity) points:

X = \frac{3}{4}

Combine real regions and undefined points for final function domain

- 4 \leq X < \frac{3}{4} or X > \frac{3}{4}

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

f (x) = - 2 x^{2} + 3 x - 3

f (x) = arcsin (ln (2 x))

f (x) = lo g_{10} (6) + 2 x

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

What is the domain of (sqrt(X+4))/(-4X+3) ?
The domain of (sqrt(X+4))/(-4X+3) is -4<= X< 3/4 \lor X> 3/4