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

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

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Answer 1 · 2014-09-13T05:11:38

In this example $g (x)$ $g(x)$ becomes the input for $f (x)$ $f(x)$ . After all of the substitutions are made foil ${(4 x - 1)}^{2}$ $(4x-1)^2$ , distribute $3 (4 x - 1)$ $3(4x-1)$ and then combine the like terms.

$(f \circ g) (x)$ $(f@g)(x)$

$f (g (x))$ $f(g(x))$

$f (4 x - 1) = {(4 x - 1)}^{2} + 3 (4 x - 1) = 16 x^{2} - 8 x + 1 + 12 x - 3 = 16 x^{2} + 4 x - 2$ $f(4x-1)=(4x-1)^2+3(4x-1)=16x^2-8x+1+12x-3=16x^2+4x-2$

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If $f (x) = x^{2}$ $f(x) = x^2$ and $g (x) = x + 2$ $g(x) = x + 2$ , what is $(f \circ g) (x)$ $(f@g)(x)$ ?

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

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