Question

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

Answer 1

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

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`