How do you find $(g o f) (- 2)$ $(gof)(-2)$ given $f (x) = - 3 x + 4$ $f(x)=-3x+4$ and $g (x) = x^{2}$ $g(x)=x^2$ ?

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Answer 1 · 2018-04-25T12:15:46

Apply definition. See below

$g \circ f (x) = g (f (x)) = g (- 3 x + 4) = {(- 3 x + 4)}^{2}$ $g@f(x)=g(f(x))=g(-3x+4)=(-3x+4)^2$

In $x = - 2$ $x=-2$ we have $g \circ f (- 2) = {(- 2 \cdot - 3 + 4)}^{2} = 10^{2} = 100$ $g@f(-2)=(-2·-3+4)^2=10^2=100$

As bonus

$f \circ g (x) = f (g (x)) = f (x^{2}) = - 3 x^{2} + 4$ $f@g(x)=f(g(x))=f(x^2)=-3x^2+4$

And for $x = - 2$ $x=-2$ we have $f \circ g (- 2) = - 3 {(- 2)}^{2} + 4 = - 8$ $f@g(-2)=-3(-2)^2+4=-8$

So composed functions are not the same and then there is no conmutativity

How do you find (gof)(−2)(gof)(-2) given f(x)=−3x+4f(x)=-3x+4 and g(x)=x2g(x)=x^2?