Answer:
y>-100 is the range.
Step-by-step explanation:
Given is the function f(x) with domain the set of all real numbers
[tex]f(x)=4^{2x} -100[/tex]
Let us substitute y =f(x)
[tex]y=4^{2x} -100[/tex]
Let us solve x in terms of y to find the range
[tex]y+100=4^{2x} \\2x log 4 = log (y+100)\\x = \frac{log(y+100)}{2log4} \\x= \frac{log(y+100)}{log16}[/tex]
Since log is defined only for non negative positive numbers excluding 0, we have y+100>0
y>-100 is the range.
