DOL (6th period)

What is the inverse of the points (1,3)(2,4)(6,2)

• (2,6)(3,1)(4,2)

• (-3,-1)(-4,-2)(-2,-6)

• (1,3)(2,4)(6,2)

• (-1,-3)(-2,-4)(-6,-2)

Answer explanation

The inverse of a point (x,y) is (y,x). Applying this to the points (1,3), (2,4), and (6,2) gives (3,1), (4,2), and (2,6) respectively. Thus, the correct answer is (2,6)(3,1)(4,2).

Find the inverse 
f(x)=2x-2
     

• f^-1(x)=1/2x+1
• f^-1(x)=-2-1/2x
• f^-1(x)=-7/3x-20/3
• 2-2/5x

Find the inverse 
f(x)=2x-2
     

• f^-1(x)=1/2x+1

• f^-1(x)=-2-1/2x

• f^-1(x)=-7/3x-20/3

• 2-2/5x

Answer explanation

To find the inverse of f(x)=2x-2, swap x and y: x=2y-2. Solve for y: y=(x+2)/2. Thus, f⁻¹(x)=1/2x+1, which matches the correct answer.

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

If the equation of f(x) goes through (1, 4) and (4, 6), what points does 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)

When finding the inverse of a relation, 
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 1/4x + 7/4
• f^-1(x) = -4x + 28
• f^-1(x) = -4x - 7
• f^-1(x) = 4x + 28

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)).  Are the two functions inverses of each other?

• x + 20 ; Yes they are inverses

• x + 20 ; No, they are not inverses

• x ; Yes they are inverses

• x ; No, they are not inverses

Answer explanation

To find f(g(x)), substitute g(x) into f: f(g(x)) = f(1/3x + 5) = 3(1/3x + 5) + 5 = x + 15 + 5 = x + 20. Since f(g(x)) ≠ x, they are not inverses. Thus, the correct choice is x + 20 ; No, they are not inverses.

Find the inverse of  $f(x)=3x+2$  

• $f^{-1}(x)=3x-2$

• $f^{-1}(x)=2+3x$

• $f^{-1}(x)=\frac{x-2}{3}$

Find the inverse of  $f(x)=4x$  

• $f^{-1}(x)=\frac{x}{4}$

• $f^{-1}(x)=4$

• $f^{-1}\left(x\right)=\frac{1}{4}$