functions

1. f(x)= sin^-1 (sin x)...find its period....

2. 2f(x²) + 3f(1/x²) = x² -1......for all x belonging to R - {0} then f(x²) = ?????

pls ans urgently required...!!!!

2 Answers

2.
replace x by 1/x
u get
2f(1/x²)+3f(x²)=1-x²/x²----(2)
2f(x²)+3f(1/x²)=x²-1-----(1)

Multiplying (1) by 3 and (2) by 2 and subtracting both the equations u arrive at ur answer!

sin^-1sinx is periodic with a period of 2âˆ©

sin^-1(sinx) =x [-âˆ©/2,âˆ©/2]
= âˆ©-x [âˆ©/2,3âˆ©/2]

so its graph will be

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