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

The domain of f(x)=(4x-1)/(sqrt(4-x)) is x<4

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domain of f(x)=(4x-1)/(sqrt(4-x))

domain

f (x) = \frac{4 x - 1}{4 - x}

x < 4

Solution steps

Find non-negative values for radicals:

x \leq 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x < 4

lo g_{10} (x + 5)

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

g (x) = \frac{x - 1}{x - 3}

\frac{2 x}{x + 1}

f (x) = t - 5

What is the domain of f(x)=(4x-1)/(sqrt(4-x)) ?
The domain of f(x)=(4x-1)/(sqrt(4-x)) is x<4