What is the domain and range of f(x)=log_(2)(-(x-3))-1 in interval notation? Domain Range (-infty ,infty ) (-infty ,infty ) (-infty ,3) (-infty ,-1) [-3,infty ) (-infty ,1] (-1,infty ) (-1,infty ) (-infty ,-1) [-1,infty ) x=-2

the domain and range of the function $f(x)=\log_{2}(-(x-3))-1$, we need to consider the restrictions on the input values (domain) and the possible output values (range).<br /><br />Domain:<br />The domain of the function is the set of all real numbers $x$ for which the argument of the logarithm, $-(x-3)$, is positive. This means that $-(x-3) > 0$, which simplifies to $x-3 < 0$. Solving this inequality, we get $x < 3$. Therefore, the domain of the function is $(-\infty, 3)$.<br /><br />Range:<br />The range of the function is the set of all possible output values. Since the logarithm function is defined for all real numbers, the range of the function is all real numbers. Therefore, the range of the function isinfty, \infty)$.<br /><br />Therefore, the domain of the function $f(x)=\log_{2}(-(x-3))-1$ is $(-\infty, 3)$, and the range is $(-\infty, \infty)$.