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

Apr 25, 2018

Apply definition. See below

#### Explanation:

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

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

As bonus

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

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

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