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AP EAMCET2008MathematicsFunctions

If f:[-6,6] R is defined by f(x)=x^2-3 for x R , then (f f f)(-1)+(f f f)(0)+(f f f)(1) is equal to

Options

  1. Af(4 2 )
  2. Bf(3 2 )
  3. Cf(2 2 )
  4. Df( 2 )

Correct answer

A. f(4 2 )

Step-by-step solution

Given, f(x)=x^2-3 Now, f(-1)=(-1)^2-3=-2 aligned & f f(-1)=f(-2)=(-2)^2-3=1 & f f f(-1)=f(1)=1^2-3=-2 aligned Now, f(0)=0^2-3=-3 aligned & f f(0)=f(-3)=(-3)^2-3=6 & f f f(0)=f(6)=6^2-3=33 aligned Again, aligned & f(1)=1^2-3=-2 & f f(1)=f(-2)=(-2)^2-3=1 & f f f(1)=(1)^2-3=-2 & f f f(-1)+f f f(0)+f f f(1) & =-2+33-2=29 & aligned Now, aligned f(4 2 ) & =(4 2 )^2-3=32-3 & =29 aligned Hence, option (a) is correct.

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