What is the domain of f(x)=log_{2}(6/(x+2)+4) ?

The domain of f(x)=log_{2}(6/(x+2)+4) is x -2

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domain of f(x)=log_{2}(6/(x+2)+4)

domain

f (x) = lo g_{2} (\frac{6}{x + 2} + 4)

x < - \frac{7}{2} or x > - 2

Interval Notation

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

Solution steps

Find positive values for logs:

x < - \frac{7}{2} or x > - 2

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

x < - \frac{7}{2} or x > - 2

f (x) = x^{2} + x, x \geq 0

f (x) = \frac{x ^{2} - 81}{x + 9}

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

f (x) = lo g_{2} (8) + 2

f (x) = lo g_{5} (4 x + 1)

What is the domain of f(x)=log_{2}(6/(x+2)+4) ?
The domain of f(x)=log_{2}(6/(x+2)+4) is x<-7/2 \lor x>-2