1 / 17

Warmup Alg 31 Jan 2012

Warmup Alg 31 Jan 2012. Agenda. Don't forget about resources on mrwaddell.net Section 6.4: Inverses of functions Using “Composition” to prove inverse Find the inverse of a function or relation. Practice from last class period’s assignment. Section 6.4: Inverses of Functions.

saxon
Download Presentation

Warmup Alg 31 Jan 2012

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. WarmupAlg31 Jan 2012

  2. Agenda • Don't forget about resources on mrwaddell.net • Section 6.4: Inverses of functions • Using “Composition” to prove inverse • Find the inverse of a function or relation

  3. Practice from last class period’s assignment.

  4. Section 6.4: Inverses of Functions

  5. Vocabulary • Domain • Range • Inverse • Composition The x values of the points The y values of the points A Function “flipped” Putting one function inside another

  6. Composition of Functions • If f(x) = 5x2 – 2x and g(x) = 4x • Then f(g(x)) is: • f(g(x)) = 5( )2 – 2( ) • g(x)g(x) f(g(x)) = 5( )2 – 2( ) • 4x4x f(g(x)) = 5(16x2 ) – 2( 4x ) f(g(x)) = 80x2 – 8x

  7. Composition of Functions 2 If f(x) = 5x2 – 2x and g(x) = 4x • Then g(f(x)) is: • g(f(x)) = 4( ) • f(x) g(f(x)) = 4( ) • 5x2 – 2x g(f(x)) = 20x2 – 8x

  8. Composition of functions 3 • If f(x)=2x and g(x) = 2x2+2 and h(x)= -4x + 3 • Find g(h(2)) g(h(2)) = 2( )2 + 2 • h(2) g(h(2)) = 2( )2 + 2 • -4(2) + 3 g(h(2)) = 2( )2 + 2 • -8 + 3 g(h(2)) = 2( -5 )2 + 2 = 52

  9. Composition of functions 3 • If f(x)=2x and g(x) = 2x2+2 and h(x)= -4x + 3 • Find h(g(2)) h(g(2)) = -4( ) + 3 • g(2) • 2(2)2 +2 h(g(2)) = -4( ) + 3 h(g(2)) = -4( )+ 3 • 2(4)+2 h(g(2)) = -4( 10 )+ 3 = -37

  10. What we are doing The inverse “flips” the picture over!

  11. Inverse # 2 Find an equation for the inverse of: y = 2x + 3 x = 2y + 3 First, switch the x and y Second, solve for y. -2y -2y -2y +x = + 3 -x -x -2y = -x + 3 -2 -2 -2 y = ½ x – 3/2 That’s all there is to it.

  12. Inverse #2 • Now you try. Find the inverse of: y = - ½x + 3 The inverse is: y = -2x + 6 Prove it! Here’s how.

  13. Verifying an inverse is true. f(x) = - ½x + 3 and the inverse is: g(x) = -2x + 6 g(f(x)) = -2( ) + 6 f(g(x)) = -½( ) + 3 • g(f(x)) = -2(-½ x + 3) + 6 • f(g(x)) = -½( -2x + 6 ) + 3 • g(f(x)) = x - 6 + 6 • f(g(x)) = x - 3 + 3 • g(f(x)) = x • f(g(x)) = x • Do (f◦g) and (g◦ f) and if they both equal “x” then they are inverses!

  14. Non-linear inverse functions The dashed line is the equation: y = x Notice the symmetry in the red and blue graphs!

  15. Non-linear inverses The dashed line is the equation: y = x Notice the symmetry in the red and blue graphs!

  16. Checking Inverses #2 • Can you show that • y = 2x + 3 and • y = ½ x – 3/2are inverses of each other? • Do f(g(x)) and g(f(x)) and if they both equal “x” then they are inverses! • Hint: Call the first one “f(x)” and the second one “g(x)” and lose the “y’s”

  17. Assignment • Section 6.4: 6-11, • 15-20, • 42-43 • Do All, and pick 1 from each group to write complete explanation.

More Related