Try for Yourself: Find the Inverse of f(x)=(-1/2)x+2

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This video encourages the viewer to find the inverse function, f^(-1)(x) if (x)=(-1/2)x+2 is given. The steps are as follows:

1. Replace f(x) with y
2. Interchange x and y
3. Solve the equation for y
4. Replace y with f^(-1)(x)
  1. John's Solution Set
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Why all this?

Find the inverse of f(x) = –½x + 2
f = –½x + 2
f – 2 = –½x
–(f – 2) = ½x
x = –2(f – 2)
thus, x(f) = –2(f – 2) is the inverse of f(x).

GirishManjunathMusic
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The intermediate of interchanging y for x is unnecessary, surely. Just solve for x instead, and declare the resultant x as a function of y, being the inverse of y as a function of x.

GirishManjunathMusic
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Bun exemplu! Curata rezolvare, Clara! Next?!

sberacatalin
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f(x)= -1/2x + 2

y = -1/2x +2
x = -1/2y +2 switch x and y , then solve for y

x-2 = -1/2 y
-2(x-2) = ( -1/2 y )-2
-2x+4 =y

devondevon