What is the domain of f(x)=sqrt((x-2)/(x-4)+3) ?

The domain of f(x)=sqrt((x-2)/(x-4)+3) is x 4

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domain of f(x)=sqrt((x-2)/(x-4)+3)

domain

f (x) = \frac{x - 2}{x - 4} + 3

x \leq \frac{7}{2} or x > 4

Interval Notation

(- \infty, \frac{7}{2}] \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq \frac{7}{2} or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq \frac{7}{2} or x > 4

e x t re m e f (x) = x^{6} e^{x} - 7

in v erse f (x) = lo g_{2} (\frac{e ^{x} - 6}{4})

mi d p o in t (- 2, - 8), (2, - 3)

d o main f (x) = \frac{x + 2}{x ^{2} - 2 x + 1}

sy mm e t ry (y - 3)^{2} = 8 (x - 5)

What is the domain of f(x)=sqrt((x-2)/(x-4)+3) ?
The domain of f(x)=sqrt((x-2)/(x-4)+3) is x<= 7/2 \lor x>4