What is the domain of f(x)=sqrt((5-2x)/(x^2-3x+2)) ?

The domain of f(x)=sqrt((5-2x)/(x^2-3x+2)) is x<1\lor 2<x<= 5/2

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domain of f(x)=sqrt((5-2x)/(x^2-3x+2))

domain

f (x) = \frac{5 - 2 x}{x ^{2} - 3 x + 2}

x < 1 or 2 < x \leq \frac{5}{2}

Solution steps

Find non-negative values for radicals:

x < 1 or 2 < x \leq \frac{5}{2}

Find undefined (singularity) points:

x = 2, x = 1

Combine real regions and undefined points for final function domain

x < 1 or 2 < x \leq \frac{5}{2}

lo g_{10} (x - 2) - 5

\frac{2 x ^{2} + 10 x - 12}{x ^{2} + x - 6}

f (x) = lo g_{7 - x} (x - 2)

lo g_{10} (16 x - x^{2})

x^{2} - 6 x + 18

What is the domain of f(x)=sqrt((5-2x)/(x^2-3x+2)) ?
The domain of f(x)=sqrt((5-2x)/(x^2-3x+2)) is x<1\lor 2<x<= 5/2