Question

The domain of f(x) = sin inverse [log to the base 9 (x square / 4 ) ] is​

Answer 1

ANSWER:

$\small{ \sf{ \text{Find \: the \: domain}}}$

$\small{ \sf{f(x) = {sin}^{ - 1}[ log_{9}( \frac{ {x}^{2} }{4} ) ]}}$

Separate the function in two parts to determine the domain of each part

$\small{ \sf{sin[ log_{9}( \frac{ {x}^{2} }{4} ) ] }} \\ \small{ \sf{ log_{9}( \frac{ {x}^{2} }{4} ) }} \\ \small{ \sf{ {x}^{2} }}$

The domain of a sine function is the set of all real numbers for sin[log_9(x²/4)]

The domain of a logarithmic function are all the values of x for which the argument is positive for

log_9(x²/4)

The domain of a quadratic function is the set of all real numbers for x²

x belongs to R

x belongs to R \{0}

x belongs to R

Find the intersection

x belongs to R \{0}