Answer:- The functions f(x) and g(x) are equivalent.
Explanation:-
Given functions:-
and ![g(x)=\sqrt[3]{64^x }](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%5B3%5D%7B64%5Ex%20%7D)
Simplify the functions by using law of exponents

Thus 
and ![g(x)=\sqrt[3]{64^x}=\sqrt[3]{(4^3)^x}= \sqrt[3]{4^{3x}}= \sqrt[3]{(4^x)^3}=4^x](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%5B3%5D%7B64%5Ex%7D%3D%5Csqrt%5B3%5D%7B%284%5E3%29%5Ex%7D%3D%20%5Csqrt%5B3%5D%7B4%5E%7B3x%7D%7D%3D%20%5Csqrt%5B3%5D%7B%284%5Ex%29%5E3%7D%3D4%5Ex)
⇒f(x)=g(x)
Therefore ,the functions f(x) and g(x) are equivalent.
Answer:
2x^2 -x +1 = 0
Step-by-step explanation:
For roots α and β, the original equation can be factored as ...
f(x) = 2(x -α)(x -β)
If we add 1 to each of those roots, the factors become ...
g(x) = 2(x -(α+1))(x -(β+1))
This can be rearranged to be ...
g(x) = 2((x -1) -α)((x -1) -β)
That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.
2(x -1)² +3(x -1) +2 = 0
2x^2 -x +1 = 0