What is the domain of f(x)=(sqrt(x+4))/(-4x+3) ?

The domain of f(x)=(sqrt(x+4))/(-4x+3) is -4 3/4

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domain of f(x)=(sqrt(x+4))/(-4x+3)

domain

f (x) = \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}

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