Math / Algebra

QuestionQuestion 8 of 10 For $f(x)=4 x+1$ and $g(x)=x^{2}-5$ , find $(f-g)(x)$ . A. $-x^{2}+4 x-4$ B. $4 x^{2}-19$ C. $-x^{2}+4 x+6$ D. $x^{2}-4 x-6$

Studdy Solution

STEP 1

1. We are given two functions $f(x) = 4x + 1$ and $g(x) = x^2 - 5$ .
2. We need to find the expression for $(f-g)(x)$ , which represents the difference between the two functions.

STEP 2

1. Write the expression for $(f-g)(x)$ .
2. Simplify the expression.

STEP 3

Write the expression for $(f-g)(x)$ :
$(f-g)(x) = f(x) - g(x) = (4x + 1) - (x^2 - 5)$

STEP 4

Distribute the negative sign and simplify the expression:
$(f-g)(x) = 4x + 1 - x^2 + 5$

STEP 5

Combine like terms:
$(f-g)(x) = -x^2 + 4x + 6$
The correct answer is:
$\boxed{-x^2 + 4x + 6}$
This corresponds to option C.

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QuestionQuestion 8 of 10 For $f(x)=4 x+1$ and $g(x)=x^{2}-5$ , find $(f-g)(x)$ . A. $-x^{2}+4 x-4$ B. $4 x^{2}-19$ C. $-x^{2}+4 x+6$ D. $x^{2}-4 x-6$

Studdy Solution

STEP 1

1. We are given two functions $f(x) = 4x + 1$ and $g(x) = x^2 - 5$ .
2. We need to find the expression for $(f-g)(x)$ , which represents the difference between the two functions.

STEP 2

1. Write the expression for $(f-g)(x)$ .
2. Simplify the expression.

STEP 3

Write the expression for $(f-g)(x)$ :
$(f-g)(x) = f(x) - g(x) = (4x + 1) - (x^2 - 5)$

STEP 4

Distribute the negative sign and simplify the expression:
$(f-g)(x) = 4x + 1 - x^2 + 5$

STEP 5

Combine like terms:
$(f-g)(x) = -x^2 + 4x + 6$
The correct answer is:
$\boxed{-x^2 + 4x + 6}$
This corresponds to option C.

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QuestionQuestion 8 of 10 For f(x)=4x+1f(x)=4 x+1f(x)=4x+1 and g(x)=x2−5g(x)=x^{2}-5g(x)=x2−5, find (f−g)(x)(f-g)(x)(f−g)(x). A. −x2+4x−4-x^{2}+4 x-4−x2+4x−4 B. 4x2−194 x^{2}-194x2−19 C. −x2+4x+6-x^{2}+4 x+6−x2+4x+6 D. x2−4x−6x^{2}-4 x-6x2−4x−6

Studdy Solution

STEP 1

1. We are given two functions f(x)=4x+1 f(x) = 4x + 1 f(x)=4x+1 and g(x)=x2−5 g(x) = x^2 - 5 g(x)=x2−5.2. We need to find the expression for (f−g)(x) (f-g)(x) (f−g)(x), which represents the difference between the two functions.

STEP 2

1. Write the expression for (f−g)(x) (f-g)(x) (f−g)(x).2. Simplify the expression.

STEP 3

Write the expression for (f−g)(x) (f-g)(x) (f−g)(x):(f−g)(x)=f(x)−g(x)=(4x+1)−(x2−5) (f-g)(x) = f(x) - g(x) = (4x + 1) - (x^2 - 5) (f−g)(x)=f(x)−g(x)=(4x+1)−(x2−5)

STEP 4

Distribute the negative sign and simplify the expression:(f−g)(x)=4x+1−x2+5 (f-g)(x) = 4x + 1 - x^2 + 5 (f−g)(x)=4x+1−x2+5

STEP 5

Combine like terms:(f−g)(x)=−x2+4x+6 (f-g)(x) = -x^2 + 4x + 6 (f−g)(x)=−x2+4x+6 The correct answer is:−x2+4x+6 \boxed{-x^2 + 4x + 6} −x2+4x+6​This corresponds to option C.

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QuestionQuestion 8 of 10 For $f(x)=4 x+1$ and $g(x)=x^{2}-5$ , find $(f-g)(x)$ . A. $-x^{2}+4 x-4$ B. $4 x^{2}-19$ C. $-x^{2}+4 x+6$ D. $x^{2}-4 x-6$

1. We are given two functions $f(x) = 4x + 1$ and $g(x) = x^2 - 5$ .
2. We need to find the expression for $(f-g)(x)$ , which represents the difference between the two functions.

1. Write the expression for $(f-g)(x)$ .
2. Simplify the expression.

Write the expression for $(f-g)(x)$ :
$(f-g)(x) = f(x) - g(x) = (4x + 1) - (x^2 - 5)$

Distribute the negative sign and simplify the expression:
$(f-g)(x) = 4x + 1 - x^2 + 5$

Combine like terms:
$(f-g)(x) = -x^2 + 4x + 6$
The correct answer is:
$\boxed{-x^2 + 4x + 6}$
This corresponds to option C.