anonymous
  • anonymous
Find an Equation for inverse function f(x)=x+9 one to one f^-1(x)=
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Inverse Functions An inverse function goes in the opposite direction! Let us start with an example: Here we have the function f(x) = 2x+3, written as a flow diagram: The Inverse Function just goes the other way: So the inverse of: 2x+3 is: (y-3)/2 The inverse is usually shown by putting a little "-1" after the function name, like this: f-1(y) We say "f inverse of y" So, the inverse of f(x) = 2x+3 is written: f-1(y) = (y-3)/2 (I also used y instead of x to show that we are using a different value.) Back to Where We Started The cool thing about the inverse is that it should give you back the original value: If the function f turns the apple into a banana, Then the inverse function f-1 turns the banana back to the apple Example: Using the formulas from above, we can start with x=4: f(4) = 2×4+3 = 11 We can then use the inverse on the 11: f-1(11) = (11-3)/2 = 4 And we magically get 4 back again! We can write that in one line: f-1( f(4) ) = 4 So applying a function f and then its inverse f-1 gives us the original value back again: f-1( f(x) ) = x We could also have put the functions in the other order and it still works: f( f-1(x) ) = x Example: Start with: f-1(11) = (11-3)/2 = 4 And then: f(4) = 2×4+3 = 11 So we can say: f( f-1(11) ) = 11 Solve Using Algebra You can also work out the inverse using Algebra. Put "y" for "f(x)" and solve for x: The function: f(x) = 2x+3 Put "y" for "f(x)": y = 2x+3 Subtract 3 from both sides: y-3 = 2x Divide both sides by 2: (y-3)/2 = x Swap sides: x = (y-3)/2 Solution (put "f-1(y)" for "x") : f-1(y) = (y-3)/2
anonymous
  • anonymous
Four steps. 1) Let f(x) = y. In this case, f(x)=x+9=y 2) f^-1(x) is implied by x=y+9 (switch x and y). 3) Solve for y. y=x-9 4) Rename y to f^-1(x) "f inverse of x" y=x-9=f^-1(x)

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