What is the domain of f(x)=(3-x)^{-7/4} ?

The domain of f(x)=(3-x)^{-7/4} is x<3

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domain of f(x)=(3-x)^{-7/4}

domain

f (x) = (3 - x)^{- \frac{7}{4}}

x < 3

Interval Notation

(- \infty, 3)

Solution steps

Find non-negative values for radicals:

x \leq 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 3

\frac{1}{5} lo g_{10} (x - 5) - \frac{2}{5}

f (x) = \frac{x + 3}{2 x - 7}

\frac{1}{2 x ^{2} + x - 6}

36 x + 49

f (x) = (4 x^{3} - 48 x^{2} + 144 x)

What is the domain of f(x)=(3-x)^{-7/4} ?
The domain of f(x)=(3-x)^{-7/4} is x<3