If f(x) = x^2 + 3xf(x)=x2+3x and g(x) = 4x - 1g(x)=4x1, what is (g@f)(x)(gf)(x)?

1 Answer
May 28, 2015

(g@f)(x)(gf)(x) (sometimes written g(f(x))g(f(x)))

can be expressed by
writing the equation for g(x)g(x)
then replacing each occurrence of xx in this equation with the expression for f(x)f(x)

g(color(red)(x)) = 4color(red)(x)-1g(x)=4x1

replacing each color(red)(x)x with the expression for f(x)f(x), namely color(blue)(x^2+3x)x2+3x

g(f(x)) = 4(color(blue)(x^2+3x))-1 g(f(x))=4(x2+3x)1

= 4x^2+12x - 1=4x2+12x1