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Math  /  Algebra

QuestionWhat is (f−g)(x)(f-g)(x) ? f(x)=−xg(x)=4x+1\begin{array}{l} f(x)=-x \\ g(x)=4 x+1 \end{array}
Write your answer as a polynomial or a rational function in simplest form.

Studdy Solution

STEP 1

1. We are given two functions, f(x) f(x) and g(x) g(x) .
2. We need to find the expression for (f−g)(x) (f-g)(x) , which means we need to subtract g(x) g(x) from f(x) f(x) .

STEP 2

1. Write the expression for (f−g)(x) (f-g)(x) .
2. Substitute the given functions into the expression.
3. Simplify the resulting expression.

STEP 3

Write the expression for (f−g)(x) (f-g)(x) :
(f−g)(x)=f(x)−g(x) (f-g)(x) = f(x) - g(x)

STEP 4

Substitute the given functions into the expression:
(f−g)(x)=(−x)−(4x+1) (f-g)(x) = (-x) - (4x + 1)

STEP 5

Simplify the expression by distributing the negative sign and combining like terms:
(f−g)(x)=−x−4x−1 (f-g)(x) = -x - 4x - 1
Combine the x x terms:
(f−g)(x)=−5x−1 (f-g)(x) = -5x - 1
The simplest form of the expression is:
−5x−1 \boxed{-5x - 1}

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