which is the range of the function $f(x)=\frac{1}{7}(9)^x$?\nall real numbers\nall real numbers less than…

Explanation:

Step1: Analyze the exponential - function form

The function is (y = f(x)=\frac{1}{7}(9)^{x}), which is an exponential function of the form (y = ab^{x}), where (a=\frac{1}{7}) and (b = 9>1).

Step2: Consider the properties of exponential functions

For any real - valued (x), the exponential function (b^{x}) where (b>0) and (b\neq1) has the property that (b^{x}>0). Here, since (b = 9>0), for all (x\in R), (9^{x}>0).

Step3: Multiply by the coefficient

Multiply (9^{x}) by (\frac{1}{7}). We get (y=\frac{1}{7}(9)^{x}). Since (9^{x}>0) and (\frac{1}{7}>0), then (\frac{1}{7}(9)^{x}>0).

Answer:

all real numbers greater than 0