# Question #5e39e

Oct 10, 2017

$15 x + 35$

#### Explanation:

I'm assuming you mean $\left(g \setminus \circ f\right)$.

$f \left(x\right) = 5 x + 9 , \setminus q \quad \setminus q \quad g \left(x\right) = 3 x + 8$

$\left(g \setminus \circ f\right) \left(x\right) \setminus \implies g \left(f \left(x\right)\right)$

So, just plug in $f \left(x\right)$ for the $x$ in $g \left(x\right)$:

$g \left(x\right) = 3 \textcolor{red}{x} + 8$

$\left(g \circ f\right) \left(x\right) = 3 \left(\textcolor{red}{5 x + 9}\right) + 8$

Now, just solve using simple algebra:

$15 x + 27 + 8$

$15 x + 35$

$\setminus \therefore \setminus q \quad \left(g \setminus \circ f\right) \left(x\right) = 15 x + 35$

Oct 10, 2017

$\left(g \circ f\right) \left(x\right) = 15 x + 35$

#### Explanation:

$\left(g \circ f\right) \left(x\right) = g \left(f \left(x\right)\right)$

In other words: replace $x$ with $f \left(x\right)$ in the function $g \left(x\right)$

$\left(g \circ f\right) \left(x\right) = 3 \left(f \left(x\right)\right) + 8$

So:

$\left(g \circ f\right) \left(x\right) = 3 \left(5 x + 9\right) + 8$

$\left(g \circ f\right) \left(x\right) = 15 x + 27 + 8$

$\left(g \circ f\right) \left(x\right) = 15 x + 35$