Question

Given f(x)=−3x+1 and g(x)=−3/x+1 , what is the value of (g∘f)(−2)?

Enter your answer, in simplest form, in the box.

(g∘f)(−2) =

Answer 1

To find the value of (g∘f)(−2), we need to first evaluate the function f(-2) and then substitute that result into the function g.

Given f(x) = -3x + 1, we can find f(-2) by substituting -2 for x:

f(-2) = -3(-2) + 1
= 6 + 1
= 7

Now, we substitute the value of f(-2) into the function g(x) = -3/x + 1:

(g∘f)(-2) = g(f(-2))
= g(7)

Given g(x) = -3/x + 1, we substitute 7 for x:

(g∘f)(-2) = -3/7 + 1

Simplifying the expression:

(g∘f)(-2) = (1 - 3/7)
= (7/7 - 3/7)
= 4/7

Therefore, (g∘f)(-2) = 4/7.