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

The domain of f(x)=arcsin((x+2)/(5-x)) is x<= 3/2

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domain of f(x)=arcsin((x+2)/(5-x))

domain

x \leq \frac{3}{2}

Interval Notation

Solution steps

Find known functions domain restrictions:

x \leq \frac{3}{2}

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x \leq \frac{3}{2}

What is the domain of f(x)=arcsin((x+2)/(5-x)) ?
The domain of f(x)=arcsin((x+2)/(5-x)) is x<= 3/2