Solveeit Logo
Login

Question

Mathematics Question on range

The domain of the function
f(x)=sin−1[2x2−3]+log2(log12(x2−5x+5))f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))
where [t] is the greatest integer function, is

A

(−52,5−√52)(-\sqrt\frac{5}{2},\frac{5-√5}{2})

B

(5−√52,5+√52)(\frac{5-√5}{2},\frac{5+√5}{2})

C

(1,5−√52)(1,\frac{5-√5}{2})

D

(1,5+√52)(1,\frac{5+√5}{2})

Answer

(1,5−√52)(1,\frac{5-√5}{2})

Explanation

Solution

The correct answer is(C): (1,5−√52)(1,\frac{5-√5}{2})

The domain of the function f\(x = sin^-1 2x^2-3+log2log_{\\frac{1}{2}}\(x^2-5x+5)) where t is the greatest integer function, is

Taking intersection

x∈(1,5−√52)x ∈(1,\frac{5-√5}{2})