Question

Let f(x)=x+4 and g(x)=x^2+8x –3. Find the function (f+g)(x), (f-g)(x), (f g)(x),  f o g

Answer 1

f(x) = x+4, g(x) = x^2+8x-3

(f+g)x = f(x)+g(x) = x+4+x^2+8x-3

= x^2+9x+1

(f-g)x = f(x)-g(x) = x+4-(x^2+8x-3)

= x+4-x^2-8x+3

= -x^2-7x+7

(fg)x = f(x)g(x)

= (x+4)(x^2+8x-3)

= x^3+8x^2-3x+4x^2+32x-12

= x^3+12x^2+29x-12

fog = f(g(x))

= f(x^2+8x-3)

= x^2+8x-3+4

= x^2+8x+1