What is the domain of f(x)=(4x+6)/(sqrt(14-7x)) ?

The domain of f(x)=(4x+6)/(sqrt(14-7x)) is x<2

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domain of f(x)=(4x+6)/(sqrt(14-7x))

domain

f (x) = \frac{4 x + 6}{14 - 7 x}

x < 2

Interval Notation

(- \infty, 2)

Solution steps

Find non-negative values for radicals:

x \leq 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2

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

f (x) = - x^{2} + 4 x

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

f (x) = - x^{2} + 5 x

x^{3} - 21

What is the domain of f(x)=(4x+6)/(sqrt(14-7x)) ?
The domain of f(x)=(4x+6)/(sqrt(14-7x)) is x<2