# Let f(x)=3x-7 and g(x)= -2x - 6, how do you find (f o g)(4)?

Oct 5, 2016

$\left(f \circ g\right) \left(4\right) = - 49$

#### Explanation:

You can solve this in two ways:
$\left(1\right) .$ plugging the $4$ into $g \left(x\right)$ and then putting what you get from that in to $f \left(x\right)$
$\left(2\right) .$ plug $g \left(x\right)$ into $f \left(x\right)$ and then plug in the $4$

Option 1:

Plug $4$ into $g \left(x\right)$:

$g \left(x\right) = - 2 \left(\textcolor{b l u e}{4}\right) - 6 = - 8 - 6 = - 14$

Then plug $g \left(x\right)$ into $f \left(x\right)$:

$f \left(x\right) = 3 \left(\textcolor{b l u e}{- 14}\right) - 7 = - 42 - 7 = - 49$

Option 2:

Plug $g \left(x\right)$ into $f \left(x\right)$:

$f \left(x\right) = 3 \left(\textcolor{b l u e}{- 2 x - 6}\right) - 7 = - 6 x - 18 - 7 = - 6 x - 25$

Finally plug $4$ into our current $f \left(x\right)$:

$f \left(x\right) = - 6 \left(\textcolor{b l u e}{4}\right) - 25 = - 24 - 25 = - 49$