Question

If $f\left(x\right)=|x|,g\left(x\right)=\left\{\begin{array}{ccc}4-(x+4{)}^2& ;& xϵ(-5,-1)\\ x^3-x^2& ;& xϵ[-1,1)\end{array}\right\}$

Number of values of x satisfying the equation f(g(f(g(x))))=0, is equal to

• A. 3
• B. 5
• C. 2
• D. 8

Answer 1

The correct option is C 2

for $f\left(g\right(f\left(g\right(x\left)\right)\left)\right)=0f\left(g\right(x\left)\right)=\left(f\right(g\left){)}^{-1}\right(0\left)f\right(g\left(x\right))=-2,0$

hence f(g(x)) =-2 has no solution
& f(g(x))=0 has value -2 & 0

so two solution only