Question

what are the domain and range of the function $f(x)=5^{x-3}+1$?○ domain: all real numbers greater than 1range: all real numbers○ domain: all real numbersrange: all real numbers greater than 0

Explanation:

Step1: Analyze the domain

The function $f(x)=5^{x-3}+1$ is an exponential function. Exponential functions accept all real numbers as input, so there are no restrictions on $x$.
Domain: All real numbers

Step2: Analyze the range

For any real number $x$, $5^{x-3} > 0$ (since exponential functions with positive base never equal or go below 0). Adding 1 to this expression gives $5^{x-3}+1 > 1$.
Range: All real numbers greater than 1

Answer:

domain: all real numbers
range: all real numbers greater than 1