Find f(x)=4x-5 and g(x)=3x^2-1, find the following functions. a. (f*g)(x); b. (g*f)(x); c. (f*g)(2)

Question

functions,f(x), g(x)

Answer 1

Given functions f(x) = 4x-5

g(x) = 3x^2-1

(f*g)(x) = f(x)g(x)

= (4x-5)(3x^2-1)

= 12x^3-4x-15x^2+5

= 12x^3-15x^2-4x+5

(f*g)(2) = 12*2^3-15*2^2-4*2+5

= 12*8-15*4-8+5

= 96-60-3

= 33

(g*f)(x)= g(x)*f(x)

= (3x^2-1)(4x-5)

= 12x^3-15x^2-4x+5

= 12x^3-15x^2-4x+5