What is the domain of f(x)=((x-8)(sqrt(x-2)))/(x-7) ?

The domain of f(x)=((x-8)(sqrt(x-2)))/(x-7) is 2 7

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domain of f(x)=((x-8)(sqrt(x-2)))/(x-7)

domain

f (x) = \frac{( x - 8 ) ( x - 2 )}{x - 7}

2 \leq x < 7 or x > 7

Interval Notation

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

2 \leq x < 7 or x > 7

g (x) = \frac{2}{x - 2}

\frac{x - 7}{8}

\frac{4 x + 9}{x + 4}

f (x) = \frac{5 x}{3 x ^{2} - 12}

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

What is the domain of f(x)=((x-8)(sqrt(x-2)))/(x-7) ?
The domain of f(x)=((x-8)(sqrt(x-2)))/(x-7) is 2<= x<7\lor x>7