anonymous
  • anonymous
If f(x) = 3x + 5, then what is f–1(x) ?
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
y = 3x+5, solve for x
amistre64
  • amistre64
or, since the inverse of (x,y) is (y,x) we can swap our a and y positions: x = 3y+5; and solve for "y" to get f-1(x)
amistre64
  • amistre64
our x and y positions ... i need a few more keys to keep track of

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anonymous
  • anonymous
soo what 5-1(3)?
anonymous
  • anonymous
let y=f(x).. then y= 3x+5; => (y-5)/3=x; ----(eq.1) => as y=f(x); => x=f-1(y); so from eq.1 (y-5)/3=f-1(y); -------(eq.2) => replace 'y' with 'x' in eq.2 then (x-5)/3= f-1(x) ----ans. thus f-1(x)=(x-5)/3 this is generalized one...u need to knw the domain and interval to restrict the limit.
amistre64
  • amistre64
5-1(3) ..... not quite x = 3y+5 -5 -5 --------- x-5 = 3y and then finish off by dividing off that 3

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