What is the domain and range of f(x)=log_(4)(x+1)+2ir inequality notation? Domain Range all real numbers xgt -1 ygt -1 xleqslant -1 ygeqslant -1 xgt 2 ygt 2 xgeqslant 2 ygeqslant 2 x=4

To determine the domain and range of the function \( f(x) = \log_{4}(x+1) + 2 \), we need to analyze the behavior of the logarithmic function.### Domain:The argument of the logarithm, , must be greater than zero because the logarithm is only defined for positive values. Therefore, we have: So, the domain of \( f(x) \) is: ### Range:The range of a logarithmic function \( \log_{4}(x+1) \) is all real numbers because as approaches from the right, \( \log_{4}(x+1) \) approaches , and as increases without bound, \( \log_{4}(x+1) \) increases without bound.Adding 2 to the logarithmic function shifts the entire range up by 2 units. Therefore, the range of \( f(x) = \log_{4}(x+1) + 2 \) is: So, the correct answers are:- Domain: - Range: