Question

I have no idea how to solve this

it is given that g(4a)= (8a-1)^2 +3 for all real values of a

a). Find g(x)
b). Find the value for g(2)
c). Find the value for g(-2)

Answer 1

`g(4a)=(8a-1)^2+3=(2(4a)-1)^2+3\\\\\text{Therefore}\ g(x)=(2x-1)^2+3\\\\\text{Put the values of x = 2 and x = -2 to the equation of the function}\\\\g(2)=(2(2)-1)^2+3=(4-1)^2+3=(3)^2+3=9+3=12\\\\g(-2)=(2(-2)-1)^2+3=(-4-1)^2+3=(-5)^2+3=25+3=28\\\\Answers:\\\\a)\ g(x)=(2x-1)^2+3\\\\b)\ g(2)=12\\\\c)\ g(-2)=28`