Home
Class 12
MATHS
Let f(x)=(x+1)^2-1, xgeq-1. Then the se...

Let `f(x)=(x+1)^2-1, xgeq-1.` Then the set `{x :f(x)=f^(-1)(x)}` is (a)`{0,1,(-3+isqrt(3))/2,(-3-isqrt(3))/2}` (b) `{0,-1}` (c)`{0,1}` (d) `e m p t y`

A

`{0, -1, (-3+isqrt(3))/(2),(-3-isqrt(3))/(2)},i=sqrt(-1)`

B

{0, 1, -1}

C

{0, -1}

D

empty

Text Solution

Verified by Experts

`f(x) = (x+1)^(2)-1" "[because xge1]`
`=x^(2)+1+2x-1=x^(2)+2x`
`S={x : f(x)-=f^(-1)(x)}`
S is the set of point of intersection of (y = x) and tf.
Now, solve y = x and `f(x) = x^(2) + 2x`
`x^(2) + 2x = x`
`x^(2) + x = 0`
x(x+1)=0
x = 0 or x = - 1
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=x^(3)/3-x^(2)/2+x-16 . Find f^(')(0), f^(')(-1) .

Let f(x)=int(1)/((1+x^(2))^(3//2))dx and f(0)=0 then f(1)=

If f(x)=(1+x)(1+x^2)(1+x^3)(1+x^4) , then f'(0)=1

Let f(x)=|cosx x 1 2sinx x2xsinx x x| , then (lim)_(x->0)(f(x))/(x^2) is equal to (a) 0 (b) -1 (c) 2 (d) 3

Let f(x)=x^3 be a function with domain {0, 1, 2, 3}. Then domain of f^(-1) is (a) {3, 2, 1, 0} (b) {0, -1, -2, -3} (c) {0, 1, 8, 27} (d) {0, -1, -8, -27}

Greatest value of f(x)=(x+1)^((1)/(3))-(x-1)^((1)/(3)) on [0,1] is 1 (b) 2( c) 3(d)(1)/(3)

If A=[[(-1+isqrt(3))/(2i),(-1-isqrt(3))/(2i)],[(1+isqrt(3))/(2i),(1-isqrt(3))/(2i)]] , I = sqrt(-1) and f (x) = x^(2) + 2, then f(A) equals to

Let f(x)={[((e^(3x)-1))/(x),,x!=0],[3,,x=0]} then 2f'(0) is

Let f(x)=x-[x],x in R,backslash then backslash f'((1)/(2)) is (3)/(2) b.1 c.0 d.-1

If f'(x)=f(x)+int_(0)^(1)f(x)dx, given f(0)=1 then the value of f((log)_(2)2) is (a) (1)/(3+e)(b)(5-e)/(3-e)(c)(2+e)/(e-2) (d) none of these