Compute Each Expression

[nycmath]

Precalculus
David Cohen
Edition 3
Chapter 3, Set 3.4

Compute each expression, given that the functions g and k are defined as shown in the attachment.

[Math Tutor]

With g(x) = x^2 - 3x - 6:

(a) (g + g)(x) = g(x) + g(x) = 2g(x) = 2x^2 - 6x - 12

(b) (g - g)(x) = g(x) - g(x) = 0 for every x (the zero function)

[Math Tutor]

(c) (kg)(x) = k(x) * g(x) = 2(x^2 - 3x - 6) = 2x^2 - 6x - 12

[nycmath]

With g(x) = x^2 - 3x - 6:

(a) (g + g)(x) = g(x) + g(x) = 2g(x) = 2x^2 - 6x - 12

(b) (g - g)(x) = g(x) - g(x) = 0 for every x (the zero function)

Thank you very much.

[nycmath]

(c) (kg)(x) = k(x) * g(x) = 2(x^2 - 3x - 6) = 2x^2 - 6x - 12

Short and simple.

[Eigenvalue]

10a. (g+g)(x)=x²-3x-6+x²-3x-6
=2x²-6x-12

10b. (g-g)(x)=x²-3x-6-(x²-3x-6)=0

10c.(kg)(x)= 2(x²-3x-6)
=2x²-6x-12

10d. (g+g)(-3)-(kg)(-3)
=2(-3)²-6(-3)-12-2(-3)²+6(-3)+12=0

[nycmath]

10a. (g+g)(x)=x²-3x-6+x²-3x-6
=2x²-6x-12

10b. (g-g)(x)=x²-3x-6-(x²-3x-6)=0

10c.(kg)(x)= 2(x²-3x-6)
=2x²-6x-12

10d. (g+g)(-3)-(kg)(-3)
=2(-3)²-6(-3)-12-2(-3)²+6(-3)+12=0

Correct. The questions here are from the Cohen book.