When answering these question, I sincerely hope that you will provide the working needed and not just write out the answer as I already have it. I just need to know the methods and steps required to acquire the answer, and that is all.
1. Given that g^-1(x) = 3-kx / 2 and f(x) = 2x^2 - 3. Find the value of k for which g(x^2) = 2f(-x).
2. If the maximum value of f(x)= -2x^2 + 3x + q is -15/8 , find the value of q.
1. Given that g^-1(x) = 3-kx / 2 and f(x) = 2x^2 - 3. Find the value of k for which g(x^2) = 2f(-x).
2. If the maximum value of f(x)= -2x^2 + 3x + q is -15/8 , find the value of q.
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1) y = 3 - kx/2 ; 2y = 6- kx--> x = (-2y + 6)/k =
g(x ) = ( -2x + 6)/k---.> g(x^2) = (-2x^2 + 6)/k = 2f(-x) = 2(2(-x)^2 -3)= 2(2x^2 - 3)
(-2x^2 + 6) = 2k(2x^2 -3) ---> k = (-2x^2 +6)/(2(2x^2 -3)) = ( k = (-x^2 +3)/(2x^2 - 3) )
2) f(x) = -2x^2 + 3x + q in the maximum or minimum the derivative = 0
d;dx( f(x)) = -4x + 3 + 0 = 0 x = (3/4)
f(3/4) = -2(3/4)^2 + 3(3/4) + q = -15/8
( -9/8) + + (9/4) + (15/8) = -q
(-9 + 18 + 15) /8 = -q
---> q = -3
g(x ) = ( -2x + 6)/k---.> g(x^2) = (-2x^2 + 6)/k = 2f(-x) = 2(2(-x)^2 -3)= 2(2x^2 - 3)
(-2x^2 + 6) = 2k(2x^2 -3) ---> k = (-2x^2 +6)/(2(2x^2 -3)) = ( k = (-x^2 +3)/(2x^2 - 3) )
2) f(x) = -2x^2 + 3x + q in the maximum or minimum the derivative = 0
d;dx( f(x)) = -4x + 3 + 0 = 0 x = (3/4)
f(3/4) = -2(3/4)^2 + 3(3/4) + q = -15/8
( -9/8) + + (9/4) + (15/8) = -q
(-9 + 18 + 15) /8 = -q
---> q = -3