2.8 - Inverse Functions

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

• (3,0) , (2, -4) , (5,5) , (6,8)

• (0,3) , (-4,2) , (5,5) , (8,-6)

• (3,2), (0, -4), (5, -6), (5,8)

Answer explanation

The inverse points are found by swapping the x and y coordinates of each point. For (3,0) it becomes (0,3), for (2,-4) it becomes (-4,2), (5,5) remains (5,5), and (-6,8) becomes (8,-6). Thus, the correct answer is (0,3), (-4,2), (5,5), (8,-6).

Tags

CCSS.HSF-BF.B.4C

Are these inverse functions?

• yes

• no

Answer explanation

Yes, these functions are inverses because applying one function followed by the other returns the original input. This confirms that they undo each other's operations.

Tags

CCSS.HSF-BF.B.4B

Are these functions inverses?

• No

• Yes

• No way to tell

Answer explanation

The functions are not inverses because they do not satisfy the condition f(g(x)) = x and g(f(x)) = x for all x in their domains. Therefore, the correct answer is 'No'.

Tags

CCSS.HSF-BF.B.4B

The inverse has been reflected over which line?

• y = x

• y =1

• y = 0

• y = x + 1

Answer explanation

The inverse of a function is obtained by reflecting its graph over the line y = x. This line represents the points where the x and y coordinates are equal, making it the correct line of reflection for finding inverses.

Tags

CCSS.HSF-BF.B.4B

Which graph represents the functions f(x) and f^-1(x)?

• 
• 
• 
• 

Tags

CCSS.HSF-BF.B.4B

Answer explanation

To find the inverse of f(x)=10+7x, swap x and y: x=10+7y. Solve for y: y=(x-10)/7. Thus, the inverse is f^{-1}(x)=\frac{x-10}{7}, which matches the correct answer.

Tags

CCSS.HSF-BF.B.4A

Answer explanation

To find the inverse, swap x and y in the equation y=(x-5)/3. This gives x=(y-5)/3. Solving for y, we get y=3x+5. Thus, the inverse is f^{-1}(x)=3x+5, which is the correct choice.

Tags

CCSS.HSF-BF.B.4A

What does it mean to find the inverse of a function?

• the x's and y's are switched

• the x's and y's are divided by 2

• the x's and y's are made negative

• the x's and y's are the same

Answer explanation

Finding the inverse of a function means switching the x's and y's. This process effectively reverses the function, allowing you to express y in terms of x and vice versa, which is correctly described by the first answer choice.

Tags

CCSS.HSF-BF.B.4A

Find the correct order to find the inverse of f(x)= 2x-5

• 2y= x+5

• y=2x-5

• 2y-5=x

Tags

CCSS.HSF-BF.B.4A

• f^-1(x) = 4x + 7

• f^-1(x) = -4x+28

• f^-1(x) = -4x - 7

• f^-1(x) = 4x+28

Answer explanation

To find the inverse, swap x and y in the equation y = (1/4)x - 7. This gives x = (1/4)y - 7. Solving for y, we get y = 4x + 28. Thus, the inverse is f^{-1}(x) = 4x + 28.

Tags

CCSS.HSF-BF.B.4A