IIT JEE , AIEEE Forum - Mathematics , Differential Calculus - some questions on functions.(Rates guaranteed)

nity

1.) If f(x) = sin^2x + sin^2(x+

/3) + cosx cos(x+

/3) and g(5/4)=1, then gof(x) is equal to ?

2.) If D is the domain if the function sec^-1(log x). then D contains?

3.) If y= [e^{sin^-1(log₂x^2)}]^1/2. then y is real in which interval.

nadeemoidu

1) f(x)=5/4 for all values of x.
therefore gof(x)=1

2) sec^-1 is defined if | logx |

1

=> x

1/e or x

e

but log x is defined for +ive values

=> x

(0,1/e] U [e,inf)

shine

3.) If y= [e^[sin^-1(log2x^2)]]1/2.
for y 2 b real

e[sin^-1(log2x^2)] >0
bt dis term is gr8er den 0 for all values for which d exponent is defined
=> -1<= log 2x^2 <=1
=> log 2x^2 >= -1 nd log 2x^2 <=1
=> e^-1 <= 2x^2 nd e>=2x^2
nd u can solve it further for values of x

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