Suppose that the functions g and h are defined for all real numbers x as follows.

g(x)=x+1

h(x)=3x^2

Write the expressions for:

(g*h)(x) = ?

(g-h)(x) = ?

(g+h)(2) = ?

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Ok when I do this I get the following answers

(g*h)(x) = (x+1)(3x^2) = 3x^3 + 3x^2

(g-h)(x) = (x+1) - 3x^2 = -3x^2 + x + 1

(g+h)(2) = (x+1) + 3x^2 = (2+1) + 3(2)^2 = 3 + 3*4 = 15

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So

(g*h)(x) = 3x^3 + 3x^2

(g-h)(x) = -3x^2 + x + 1

(g+h)(2) = 15

Are these final answers correct?