JEE Main 2024 Mathematics question
Let f(x) = x⁵ + 2x³ + 3x + 1, x ∈ R, and g(x) be a function such that g(f(x)) = x for all x ∈ R. Then is equal to:
Answer: (D)
Solution
f(1) = 7, so g(7) = 1; g′(7) = 1/f′(1) = 1/(5 + 6 + 3) = 1/14, and the ratio is 14.