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Math  /  Algebra

QuestionIf f(x)=x2−6x+2f(x)=x^{2}-6 x+2 and g(x)=−2xg(x)=-2 x, find the following composition. (g∘f)(−1)(g∘f)(−1)=□\begin{array}{l} (g \circ f)(-1) \\ (g \circ f)(-1)=\square \end{array}

Studdy Solution

STEP 1

1. We are given the functions f(x)=x2−6x+2 f(x) = x^2 - 6x + 2 and g(x)=−2x g(x) = -2x .
2. We need to find the composition (g∘f)(−1) (g \circ f)(-1) .

STEP 2

1. Evaluate f(−1) f(-1) .
2. Use the result from Step 1 as the input for g(x) g(x) .
3. Evaluate g(f(−1)) g(f(-1)) .

STEP 3

Substitute x=−1 x = -1 into f(x) f(x) :
f(−1)=(−1)2−6(−1)+2 f(-1) = (-1)^2 - 6(-1) + 2

STEP 4

Simplify the expression:
f(−1)=1+6+2 f(-1) = 1 + 6 + 2 f(−1)=9 f(-1) = 9

STEP 5

Now that we have f(−1)=9 f(-1) = 9 , substitute this result into g(x) g(x) :
g(f(−1))=g(9) g(f(-1)) = g(9)

STEP 6

Substitute x=9 x = 9 into g(x) g(x) :
g(9)=−2(9) g(9) = -2(9)

STEP 7

Simplify the expression:
g(9)=−18 g(9) = -18
The value of (g∘f)(−1) (g \circ f)(-1) is:
−18 \boxed{-18}

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