Question
If g(x)=x^2+x-2 and 1 2 g o f(x)=2 x^2-5 x+2 then f(x) is equal to
BITSAT
Mathematics
Functions
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 2 x-3
- B. 2 x+3
- C. 2 x^2+3 x+1
- D. 2 x^2-3 x+1
Answer
A. 2 x-3
Step-by-step solution
We have, 1 2 go f(x)=2 x^2-5 x+2 aligned & g(f(x))=4 x^2-10 x+4 \\ & (f(x))^2+f(x)-2=4 x^2-10 x+4 \\ & (f(x))^2+f(x)- (4 x^2-10 x+6 )=0 \\ & f(x)= -1 1+4 (4 x^2-10 x+6 ) 2 \\ & f(x)= -1 16 x^2-40 x+25 2 \\ & f(x)= -1 (4 x-5) 2 =2 x-3,-2 x+2 aligned Hence, f(x)=2 x-3
Related: Mathematics — Functions · All PYQ Banks