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KCET2023MathematicsFunctions

Let f(x)= 2 x+ 2 x and g(x)=x^2-1 then g(f(x)) is invertible in the domain

Options

  1. Ax [ - 8 , 8 ]
  2. Bx [ - 2 , 2 ]
  3. Cx [0, 4 ]
  4. Dx [ - 4 , 4 ]

Correct answer

A. x [ - 8 , 8 ]

Step-by-step solution

f(x)= 2 x+ 2 x and g(x)=x^2-1 aligned & g[f(x)]= [( 2 x+ 2 x)^2-1 ] & g[f(x)]= ^2 2 x+ ^2 2 x+ 4 x-1 & g[f(x)]= 4 x & Let g f(x)=y aligned y= 4 x [ . Domain of x is .- 2 , 2 ] Domain of 4 x= [- 8 , 8 ]

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