what is the domain of the following functions

1. 1/sqrt(4x-|x^2 -10x +9|)

2. sin-1 (1/|x^2 -1|) + 1/sqrt(sin^2 x +sinx +1)

3. squt(sin-1 (3x-4x^3)) +squt(cos-1 (x))

cos-1 is cos inverse of sin-1 is sin inverse of ^represents to the power

Dear Student,
Please find below the solution to the asked query:

y=14x-x2-10x+9=14x-x2-x-9x+9=14x-xx-1-9x-1=14x-x-1x-9By method of interval:+++++ 1 ---- 9 ++++x-1x-9>0 when x<1 or x>9x-1x-9<0 when x1,9x-1x-9=x-1x-9=x2-10x+9 x<1 or x>9-x-1x-9=-x2-10x+91x9Case i x<1 or x>9y=14x-x2-10x+9=14x-x2+10x-9=1-x2+14x-9For root to be defined-x2+14x-9>0-x2-14x+9>0x2-14x+9<0x2-14x+49-49+9<0x-72-40<0x-72-2102<0x-7-210x-7+210<0x-7+210x-7-210<0x7-210,7+210Taking intersection common with  x<1 or x>9, we get:x7-210,19,7+210...iCaseii 1x9y=14x--x2-10x+9=14x+x2-10x+9=1x2-6x+9=1x-32Now x-32>0 for all values of x, except x=3xR-3Taking intersection with 1x9, we get:x1,9-3...iiTaking union of i and ii, we get:x7-210,7+210-3Please ask only one question in one thread.

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