Question

For f(x)=x+3 and g(x)=4x+5 find the following functions(simplify answers)

(f*g)(x)=

(g*f)(x)=

(f*g)(-1)=

Answer 1

`(f * g)(x) = (x + 3)(4x + 5) \\(f * g)(x) = x(4x + 5) + 3(4x + 5) \\(f * g)(x) = x(4x) + x(5) + 3(4x) + 3(5) \\(f * g)(x) = 4x^(2) + 5x + 12x + 15 \\(f * g)(x) = 4x^(2) + 17x + 15`


`(g * f)(x) = (4x + 5)(x + 3) \\(g * f)(x) = 4x(x + 3) + 5(x + 3) \\(g * f)(x) = 4x(x) + 4x(3) + 5x(x) + 5(3) \\(g * f)(x) = 4x^(2) + 12x + 5x + 15 \\(g * f)(x) = 4x^(2) + 17x + 15`


`(f * g)(-1) = (-1 + 3)(4(-1) + 5) \\(f * g)(-1) = (2)(-4 + 5) \\(f * g)(-1) = (2)(1) \\(f * g)(-1) = 2`