Question
f(x)= x+ x, g(x)=x^2-1, then g(f(x)) is invertible if
BITSAT
Mathematics
Functions
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. - 4 x 4
- B. - 2 x 0
- C. - 2 x
- D. 0 x 2
Answer
A. - 4 x 4
Step-by-step solution
Given that, f(x)= x+ x g(x)=x^2-1 g[f(x)]=( x+ x)^2-1 = ^2 x+ ^2 x+2 x x-1 =1+ 2 x-1= 2 x ( ^2 x+ ^2 x=1, x=2 x x ) Among the given options, 2 x is monotonous (here strictly increasing) in - 4 x 4 . So, g(f(x)) is invertible in - 4 x 4 .
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