You can simplify both the given function first to see how are they related.
Both the functions f(x) and g(x) are same. Thus their graph will be same(exponential graph)
A function sometimes can be solved further to make it more simple to operate on. This is called simplifying the function; and the process is called simplification.
We ca see if we can cancel out those roots.
For function f(x):
[tex]f(x) = (\sqrt{16})^x = (\sqrt{4 \times 4})^x = (\sqrt{4^2})^x = 4^x\\ f(x) = 4^x[/tex] (square root canceled out by 2 as power of 4)
Similarly for g(x):
[tex]g(x) = \: ^3\sqrt{64})^x = (^3\sqrt{4 \times 4 \times 4})^x = (^3\sqrt{4^3})^x = 4^x\\ g(x) = 4^x[/tex](cube root canceled out by 3 as power of 4)
(nth root cancels out if the quantity which is inside it is fully raised to power n)
Thus, we have both f(x) and g(x) same. They both are exponential function as the variable x is exponent of constant 4 which both together represent the functions f(x) and g(x).
Their graph will be same, [tex]4^x[/tex], as shown below.
Learn more about simplifying functions here:
https://brainly.com/question/10781706
Answer:
the function f(x) and g (x) are equivalent
Step-by-step explanation:
edge 2022 just took the quiz
Hope it helps!!
