The range of the function given below is the set of all positive real numbers greater than 7. \[ F(x)=7+3^{x} \] A. True B. False

Step 1 ：The function is a sum of a constant and an exponential function. The exponential function \(3^x\) is always positive for any real number x. Therefore, the function \(F(x) = 7 + 3^x\) will always be greater than 7 for any real number x.

Step 2 ：We need to check if there are any values of x for which the function \(F(x)\) equals 7. If there are, then the statement would be false because the range of the function would also include 7, not just numbers greater than 7.

Step 3 ：The solution set is empty, which means there are no real values of x for which the function \(F(x)\) equals 7. Therefore, the range of the function is indeed all positive real numbers greater than 7.

Step 4 ：Final Answer: \(\boxed{\text{A. True}}\)