G(x)=2x+7
H(x)=1/(x+2)
1) H(G(x))=
J: y=-3x^2
2) J(H(x))=
3) J/H=
To find the value of H(G(x)), we substitute G(x) into the expression for H(x):
H(G(x)) = 1 / (G(x) + 2)
Since G(x) is given as 2x + 7, we substitute that into the expression:
H(G(x)) = 1 / (2x + 7 + 2)
Simplifying the expression:
H(G(x)) = 1 / (2x + 9)
So, the answer to 1) is H(G(x)) = 1 / (2x + 9).
To find J(H(x)), we substitute H(x) into the expression for J:
J(H(x)) = -3(H(x))^2
Since H(x) is given as 1 / (x + 2), we substitute that into the expression:
J(H(x)) = -3(1 / (x + 2))^2
Simplifying the expression:
J(H(x)) = -3 / (x + 2)^2
So, the answer to 2) is J(H(x)) = -3 / (x + 2)^2.
To find J/H, we divide the expression for J by the expression for H:
J/H = J(x) / H(x)
Substituting the given expressions for J(x) and H(x):
J/H = (-3x^2) / (1 / (x + 2))
Inverting the denominator and multiplying:
J/H = (-3x^2) * (x + 2)
Expanding the expression:
J/H = -3x^3 - 6x^2
So, the answer to 3) is J/H = -3x^3 - 6x^2.