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.

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.

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.

Match each function composition with its result.

• (f o g)(x) for f(x) = x² + 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

• 50x² - 20x - 3

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

• 25x² - 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.

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.

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.

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.

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.

Match each function with its inverse.

• f(x) = 4/9(x + 3)

• f^(-1)(x) = 4/9x + 3

• f(x) = 9/4(x - 3)

• f^(-1)(x) = 9/4x - 3

• f(x) = 9/4(x + 3)

• f^(-1)(x) = 9/4x + 3

• f(x) = 4/9(x - 3)

• f^(-1)(x) = 4/9x - 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.