Question

For funcitons f(x)=2x+3 and g(x)=-3x-2, please find (f∘g)(-1)

Answer 1

Answer:

$\displaystyle (f\circ g)(-1) = 5$

Step-by-step explanation:

We are given the two functions:
$\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2$

And we want to find:
$\displaystyle (f\circ g)(-1)$

Recall that this is equivalent to:
$\displaystyle (f\circ g)(-1) = f(g(-1))$

Hence, find g(-1):
$\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}$

Substitute:
$\displaystyle f(g(-1)) = f(1)$

Find f(1):

$\displaystyle \begin{aligned} f(x) & = 2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}$

In conclusion:
$\displaystyle (f\circ g)(-1) = 5$