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

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Answer 1 · 2015-05-28T00:16:16

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

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

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

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

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

$= 4x^2+12x - 1$

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