Question

If f(x) = 134 -6 + 12x4-5x8 +6x?) (1 – x2), find complete values of x, for which fx is real x + 2

JEE/Engineering Exams

Maths

Solution

126

4.0 (1 ratings)

( Q rightarrow f(x)=sqrt{frac{3 x-6}{x+2}}+sqrt[4]{left(x^{4}-5 x^{3}+6 x^{2}right)left(1-x^{2}right)} ) Ans ( rightarrow f(x) ) will be real iffothe Denominator ( eq 0 ) ( Rightarrow(2) ) The value under root is greater than "O" zero all the time ( therefore ) For, ( sqrt{frac{3 x-6}{x+2}} rightarrow x eq-2 ) ( (2)^{N 000}: frac{3 x-6}{x+2}>0 ) always, for ( f(x) ) to be real Noos, ( quad ) Grayh of ( frac{3 x-6}{x+2} ) is ( underset{-v e}{operatorname{tre}} longleftrightarrow underbrace{Delta}_{2} x ) -axis ( therefore quad x in(-infty,-2) cup(2, infty) ) ( (3)^{N_{0} omega}, quadleft(x^{4}-5 x^{3}+6 x^{2}right)left(1-x^{2}right)>0 ) be real ( _{1}, f_{0}+f(x) ) to ( x^{2}left(x^{2}-5 x+6right)left(1-x^{2}right)>0 ) ( x^{2}(1+x)(1-x)(x-2)(x-3)>0 ) Graph of this is tye ( therefore x in(-infty,-1) cup(0,1) cup(2,3) ) COMBINING ( operatorname{eq} underline{n} quad(mathbb{D}, mathbb{Q} & widehat{3}) ) [ x in(-infty,-2) cup ] (2,3)( quad ) Arswer