# Let f(x) = 3x - 4 and g(x) = x^2 - 2, what is the value of f(g(2)) and f(g(x))?

Mar 4, 2016

$\textcolor{b l u e}{f \left(g \left(2\right)\right) = 2}$
$\textcolor{w h i t e}{.}$
$\textcolor{b l u e}{g \left(f \left(x\right)\right) = - 15 x + 14}$

#### Explanation:

Assuming you mean:
$f \left(x\right) = 3 x - 4$
$g \left(x\right) = {x}^{2} - 2$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To determine } f \left(g \left(2\right)\right)}$

$g \left(2\right) = {2}^{2} - 2 \text{ " =" "4-2" "=" } 2$

$f \left(g \left(2\right)\right) = 3 \left(2\right) - 4 \text{ " =" "6-4" "=" } 2$

$\textcolor{b l u e}{f \left(g \left(2\right)\right) = 2}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To determine } g \left(f \left(x\right)\right)}$

Given that $f \left(x\right) = 3 x - 4$ then

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

$g \left(f \left(x\right)\right) = \left(9 x - 24 x + 16\right) - 2$

$\textcolor{b l u e}{g \left(f \left(x\right)\right) = - 15 x + 14}$