+√x+7, we need to consider the constraints imposed by both components of the function: The term ‌
1
log10(3−x)
requires log10(3−x) to be a defined, non-zero value. The logarithm log10(3−x) is defined when 3−x is positive, so: 3−x>0‌‌⇒‌‌x<3 Also, log10(3−x)≠0, which implies: log10(3−x)=0‌‌⇒‌‌3−x=1‌‌⇒‌‌x=2 Thus, x≠2. The term √x+7 requires the argument inside the square root to be non-negative: x+7≥0‌‌⇒‌‌x≥−7 Combining these constraints, we get: ‌−7≤x<3 ‌x≠2 Thus, the domain of the function is the interval [−7,3) excluding x=2. This corresponds to Option C . So, the correct answer is: Option C [−7,3)−{2}