Dear student, A fx =sgnx+1domain x∈Rrange fx =sgnx+1x+1≥1 thenfx =sgnx+1 =1fx∈1B fx =sin2lnx+cos2lnx domain x∈0,∞range fx =sin2lnx+cos2lnx use sin2x+cos2x=1x+1≥1 thenfx =1fx∈1C fx =2πsin-1x+cos-1xdomain x∈Rrange use sin-1x+cos-1x=π2fx =2π×π2=1fx∈1D fx =sec2x-tan2xdomain x∈Rrange use x=0=x fx =sec20-tan20fx∈1 answer A,C,D Hope this information will clear your doubts If you have any more doubts just ask here on the forum and our experts will try to help out as soon as possible Regards

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Solve this: 10. Which of the following are identical functions ? f(x) = sgn(lxl + I) —— sin-I {x} +cos- x (where [xJ denotes greatest integer less than or equal x, denotes si um function of x respectively.) sin (Inx)+cos (Inx) sec2 — tare (x) denotes fractional part of

Dear student,

A . f (x) = s g n (|x| + 1) d o m a i n x \in R r a n g e f (x) = s g n (|x| + 1) |x| + 1 \geq 1 t h e n f (x) = s g n (|x| + 1) = 1 f (x) \in \{1\} B . f (x) = \sin^{2} (\ln x) + \cos^{2} (\ln x) d o m a i n x \in (0, \infty) r a n g e f (x) = \sin^{2} (\ln x) + \cos^{2} (\ln x) u s e \sin^{2} x + \cos^{2} x = 1 |x| + 1 \geq 1 t h e n f (x) = 1 f (x) \in \{1\} C . f (x) = \frac{2}{π} (\sin^{- 1} \{x\} + \cos^{- 1} \{x\}) d o m a i n x \in R r a n g e u s e \sin^{- 1} x + \cos^{- 1} x = \frac{π}{2} f (x) = \frac{2}{π} \times \frac{π}{2} = 1 f (x) \in \{1\} D . f (x) = s e c^{2} [\{x\}] - \tan^{2} \{[x]\} d o m a i n x \in R r a n g e u s e [\{x\}] = 0 = \{[x]\} f (x) = s e c^{2} 0 - \tan^{2} 0 f (x) \in \{1\}

answer A,C,D
Hope this information will clear your doubts. If you have any more doubts just ask here on the forum and our experts will try to help out as soon as possible.
Regards

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Solve this: Solve this: 10. Which of the following are identical functions ? f(x) = sgn(lxl + I) —— sin-I {x} +cos- x (where [xJ denotes greatest integer less than or equal x, denotes si um function of x respectively.) sin (Inx)+cos (Inx) sec2 — tare (x) denotes fractional part of

Solve this:

Solve this: 10. Which of the following are identical functions ? f(x) = sgn(lxl + I) —— sin-I {x} +cos- x (where [xJ denotes greatest integer less than or equal x, denotes si um function of x respectively.) sin (Inx)+cos (Inx) sec2 — tare (x) denotes fractional part of