AP EAMCET202317 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
Match the ranges of the functions given in List - I with those of the items given in List - II
Options
- A(1) (c) (II) (a) (III) (d) (IV) (b)
- B(1) (c) (II) (d) (III) (a) (IV) (b)
- C(1) (b) (II) (d) (III) (a) (IV) (e)
- D(1) (b) (II) (e) (III) (d) (IV) (c)
Correct answer
B. (1) (c) (II) (d) (III) (a) (IV) (b)
Step-by-step solution
(I) aligned 3 ^2 x+4 ^2 x-2 & =3 ^2 x+3 ^2 x+ ^2 x-2 & =3+ ^2 x-2= ^2 x+1 aligned Also, 0 ^2 x 1 1 ^2 x+1 2 1 3 ^2 x+4 ^2 x-2 2 Range of (3 ^2 x+4 ^2 x-2 ) is [1,2] aligned & (II) ^2 x+ ^4 x= ^2 A+ (1- ^2 A )^2 & = ^2 A+1+ ^4 A-2 ^2 A & =- ^2 A+1+ ^4 A & =- ^2 A (1- ^2 A )+1 & =1- ^2 A ^2 A & =1- ( 2 A 2 )^2 & 0 ^2 2 x 1 0 ^2 2 x 4 1 4 & 0 - [ 2 x 2 ]^2 - 1 4 & 1 1- [ 2 x 2 ]^2 1- 1 4 & 1 ^2 A+ ^4 x 3 4 aligned aligned & (III) ^6 x+ ^6 x= ( ^2 x )^3+ ( ^2 x )^3 & = ( ^2 x+ ^2 x )^3-3 ^2 x ^2 x ( ^2 x+ ^2 x ) & =1-3