13A={0,-1}
Let f:R→R be given by f(x) =(x+1)2 - 1 where x ≥ -1 .If A= {x:f(x)=f-1(x)} ,then A=?
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14 Answers
1f(x) = x2 + 2x = y[say]
=> x2 +2x -y =0
=> x = (-2 ± √4-4y)/2 => -1±√1-y
=> f-1(x) = -1 ± √1-x
now
A : f(x) =f-1(x) => f(x)-f-1(x) = 0
=> x2 +2x - [-1 ± √1-x ] = 0
=> (x+1)2 = ± √1-x
now plot grahp ...
1357one more method
look it if its useful
f-1(x) is the image of f(x) about y=x line
now f(x)=f-1(x) gives the point of intersection of these curves
that means image and object coincides
so this will happen only when the object is on y=x line
so f(x)=x will also give the point of intersection
x=(1+x)2-1
1wow!
but y am i not getting -1 ??
bhaiya plz chcek where is it wrong ...
1357in the roots of quadratic eqaution
you have made a mistake in calculating D=√(b2-4ac)
1arey i was wrong ...
hadbadi me gadbadi ... (nishant bhaiya dekhne se phirse ...i will be bashed [2])
u are right .. it is 0, -1 .
13do it.... simple
y=(x+1)2 - 1
±√y+1=x+1
±√y+1-1=x
hence
±√x+1-1=f-1(x)
33galti se sahi hua :P
@so this will happen only when the object is on y=x line
remove only from it...