Question
If f: R R, g: R R are defined by f(x)=5 x- 3, g(x)=x^2+3, then g o f^ -1 (3) is equal to
BITSAT
Mathematics
Functions
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 25 3
- B. 111 25
- C. 9 25
- D. 25 111
Answer
B. 111 25
Step-by-step solution
Given, f(x)=5 x-3 and g(x)=x^2+3 Let, y=f(x), y=5 x-3 y+3=5 x x= y+3 5 f^ -1 (y)= y+3 5 f^ -1 (x)= x+3 5 Now, g(x)=x^2+3 So, g f^ -1 (3)=g [f^ -1 (3) ] =g ( 3+3 5 )=g ( 6 5 )= (6)^2 (5)^2 +3= 36 25 +3= 111 25
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