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

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

x \leq \frac{3}{2}

Interval Notation

(- \infty, \frac{3}{2}]

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}

f (x) = 1650 ((1.022))^{t}

\frac{5}{x}

f (x) = \frac{x - 8}{x ^{2} + x - 72}

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

f (x) = x^{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