Chapter 5 Mid-Chapter Quiz

(f + g)(x) = (a)   , where f(x) = 2x² + 4x - 3 and g(x) = 5x - 2.

• 2x2 + 9x - 5
• 2x² + 4x - 5

• 2x² + 9x - 1

• 2x² + 4x - 1

Answer explanation

To find (f + g)(x), add f(x) and g(x): (2x^2 + 4x - 3) + (5x - 2) = 2x^2 + 9x - 5. Thus, the correct answer is 2x^2 + 9x - 5.

Tags

CCSS.HSF-BF.A.1B

Given f(x) = 2x² + 4x - 3 and g(x) = 5x - 2, find (f - g)(x).

• 2x² + 4x - 3 - (5x - 2)

• 2x² + 4x - 3 - 5x + 2

• 2x² - x - 1

• 2x² - x - 5

Answer explanation

To find (f - g)(x), subtract g(x) from f(x): 2x^2 + 4x - 3 - (5x - 2) simplifies to 2x^2 + 4x - 3 - 5x + 2, which further simplifies to 2x^2 - x - 1. Thus, the correct answer is 2x^2 - x - 1.

Tags

CCSS.HSF-BF.A.1B

Given f(x) = 2x² + 4x - 3 and g(x) = 5x - 2, find (f * g)(x).

• 10x³ + 20x² - 23x - 6

• 10x³ + 20x² - 8x + 6

• 10x³ + 16x² - 23x + 6

• 10x³ + 20x² - 6x + 6

Answer explanation

To find (f * g)(x), multiply f(x) and g(x): (2x^2 + 4x - 3)(5x - 2). This results in 10x^3 + 20x^2 - 10x - 6. Combining like terms gives 10x^3 + 20x^2 - 23x + 6, matching the correct answer.

Tags

CCSS.HSF-BF.A.1B

Match each function composition with its result.

• (f o g)(x) for f(x) = 2x² + 4x - 3 and g(x) = 5x - 2

• 10x² - 20x + 7

• (f o g)(x) for f(x) = 2x² + 4x - 3 and g(x) = x - 2

• 25x² - 20x + 3

• (f o g)(x) for f(x) = x² + 4x - 3 and g(x) = 5x - 2

• 50x² - 20x - 3

Answer explanation

To find (f o g)(x), substitute g(x) into f(x): f(g(x)) = f(5x - 2) = 2(5x - 2)^2 + 4(5x - 2) - 3. Expanding this gives 50x^2 - 20x - 3, which matches the correct answer.

Tags

CCSS.HSF-BF.A.1C

Given f(x) = 2x² + 4x - 3 and g(x) = 5x - 2, find (g o f)(x).

• 10x² + 20x - 8

• 10x² + 20x - 13

• 10x² + 20x - 17

Answer explanation

To find (g o f)(x), substitute f(x) into g(x): g(f(x)) = g(2x^2 + 4x - 3) = 5(2x^2 + 4x - 3) - 2 = 10x^2 + 20x - 15 - 2 = 10x^2 + 20x - 17. Thus, the correct answer is 10x^2 + 20x - 17.

Tags

CCSS.HSF-BF.A.1C

Determine whether each pair of functions are inverse functions. Write yes or no.

f(x) = 2x + 16

g(x) = 1/2x - 8

• Yes

• No

Answer explanation

To check if f(x) and g(x) are inverses, we can compose them: f(g(x)) = f(1/2x - 8) = 2(1/2x - 8) + 16 = x. Since f(g(x)) = x, they are indeed inverse functions. Thus, the answer is Yes.

Tags

CCSS.HSF-BF.B.4B

Determine whether each pair of functions are inverse functions. The answer is (a)   .

f(x) = x² - 5

g(x) = 5 + x^-2

• yes

• no

Answer explanation

To check if f(x) and g(x) are inverses, we need to see if f(g(x)) = x and g(f(x)) = x. Calculating these shows they do not equal x, thus they are not inverse functions. The answer is no.

Tags

CCSS.HSF-BF.B.4B

Determine whether each pair of functions are inverse functions. Write yes or no.

g(x) = -6x + 8

h(x) = (8 - x)/6

• yes

• no

Answer explanation

To check if g(x) and h(x) are inverses, we verify if g(h(x)) = x and h(g(x)) = x. Calculating both gives x, confirming they are inverses. Thus, the answer is yes.

Tags

CCSS.HSF-BF.B.4B

Find the inverse of each function, if it exists.

h(x) = 2/5x + 8

• h⁻¹(x) = 5/2x - 8

• h⁻¹(x) = 5/2x + 8

• h⁻¹(x) = 5/2(x - 8)

• h⁻¹(x) = 5/2(x + 8)

Answer explanation

To find the inverse, swap x and y in h(x) = 2/5x + 8, giving x = 2/5y + 8. Solving for y yields y = 5/2(x - 8). Thus, h⁻¹(x) = 5/2(x - 8) is the correct choice.

Tags

CCSS.HSF-BF.B.4A

Match each function with its inverse.

• f(x) = 9/4(x + 3)

• f^(-1)(x) = 4/9x - 3

• f(x) = 4/9(x - 3)

• f^(-1)(x) = 9/4x - 3

• f(x) = 4/9(x + 3)

• f^(-1)(x) = 4/9x + 3

• f(x) = 9/4(x - 3)

• f^(-1)(x) = 9/4x + 3

Answer explanation

To find the inverse, swap x and y in f(x) = 4/9(x - 3). This gives x = 4/9(y - 3). Solving for y yields y = 9/4x + 3. Thus, f^(-1)(x) = 9/4x + 3, which is the correct choice.

Tags

CCSS.HSF-BF.B.4A