To find the composition functions, we substitute the given functions into each other according to the provided equations.
H(f(x))H(f(x)) = H(-2x"+3x-5H(f(x)) = 2(-2x"+3x-5) - (-2x"+3x-5)"-H(f(x)) = -4x"+6x-10 + 3x-5-H(f(x)) = -4x"+9x-18
f(4(x))f(4(x)) = -2(4x+2)"+3(4x+2)-f(4(x)) = -2(4x+2)" + 12x+6 - f(4(x)) = -32x" - 12x - 4 + 12x+6 - f(4(x)) = -32x" - 1
Therefore, the compositions are:
To find the composition functions, we substitute the given functions into each other according to the provided equations.
H(f(x))
H(f(x)) = H(-2x"+3x-5
H(f(x)) = 2(-2x"+3x-5) - (-2x"+3x-5)"-
H(f(x)) = -4x"+6x-10 + 3x-5-
H(f(x)) = -4x"+9x-18
f(4(x))
f(4(x)) = -2(4x+2)"+3(4x+2)-
f(4(x)) = -2(4x+2)" + 12x+6 -
f(4(x)) = -32x" - 12x - 4 + 12x+6 -
f(4(x)) = -32x" - 1
Therefore, the compositions are:
H(f(x)) = -4x"+9x-18f(4(x)) = -32x" - 1