Unit 6 Test Review - Compositions and Inverses

f(x) = 2x - 5

g(x) = -4x - 2

Find f(g(-2))

• 25

• -25

• -7

• 7

Answer explanation

First, calculate g(-2): g(-2) = -4(-2) - 2 = 8 - 2 = 6. Then, find f(6): f(6) = 2(6) - 5 = 12 - 5 = 7. Thus, f(g(-2)) = 7.

Tags

CCSS.HSF-BF.A.1C

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

• 10x-1

• 10x-5

• 5x²-1

• 5x²-5

Answer explanation

To find f(g(x)), substitute g(x) into f(x): f(g(x)) = f(2x-1) = 5(2x-1) = 10x - 5. Thus, the correct answer is 10x-5.

Tags

CCSS.HSF-BF.A.1C

• 34

• 71

• 35

• 142

Answer explanation

First, calculate g(3): g(3) = 2(3^2) - 1 = 2(9) - 1 = 18 - 1 = 17. Then, find f(g(3)): f(17) = 2(17) = 34. Thus, the answer is 34.

Tags

CCSS.HSF-BF.A.1C

Find the inverse: f(x) = 3x + 2

• f^-1(x) = 2x + 3

• f^-1(x) = -3x + 2

• f^-1(x) = (x-2)/3

• f^-1(x) = (x-3)/2

Answer explanation

To find the inverse of f(x) = 3x + 2, swap x and y: x = 3y + 2. Solve for y: y = (x - 2)/3. Thus, f^-1(x) = (x - 2)/3, which is the correct choice.

Tags

CCSS.HSF-BF.B.4A

To graph the inverse of a function...

• Rotate it around the origin

• Reflect it across the x-axis

• Reflect it across the y-axis

• Switch the x and y coordinates and plot the new points

Answer explanation

To graph the inverse of a function, you switch the x and y coordinates of each point on the original graph. This reflects the graph across the line y=x, which is the correct method for finding the inverse.

Tags

CCSS.HSF-BF.B.4C

• A.
• B.
• C.
• D.

Tags

CCSS.HSF-BF.B.4A

A function, f(x), goes through (1, 4) and (4, 6), what points below does it's inverse f^-1(x) go through?

• (1, 4) and (4, 6)

• (-4, -1) and (-6, -4)

• (-1, -4) and (-4, -6)

• (4, 1) and (6, 4)

Answer explanation

The inverse function f^-1(x) swaps the coordinates of the points on f(x). Therefore, the points (1, 4) and (4, 6) on f(x) correspond to (4, 1) and (6, 4) on f^-1(x). Thus, the correct answer is (4, 1) and (6, 4).

Tags

CCSS.HSF-BF.B.4C

Answer explanation

To find \( (f \circ g)(x) \), substitute \( g(x) \) into \( f(x) \): \( f(g(x)) = f(x^2 - 3x + 8) = 2(x^2 - 3x + 8) - 5 = 2x^2 - 6x + 16 - 5 = 2x^2 - 6x + 11 \). Thus, the correct answer is \( 2x^2 - 6x + 11 \).

Tags

CCSS.HSF-BF.A.1C

Identify all pairs of inverse functions from their graphs.

• 
• 
• 
• 

Tags

CCSS.HSF-BF.B.4C

Given f and g in the graph,

what is f(g(2)) ?

• 3

• 8

• 1

• 4

Answer explanation

To find f(g(2)), first determine g(2) from the graph, which is 4. Then, find f(4) from the graph, resulting in 1. Thus, f(g(2)) = 1.

Tags

CCSS.HSF-BF.A.1C