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Mathematics · 2023

JEE Main · 25 January 2023, Shift 1 · Q81

For some a, b, c ∈ N, let f(x)=a x-3 and g(x)=x^b+c, x ∈ R. If (f ° g)^-1(x)=((x-7)/2)^1 / 3, then (f ° g)(a c)+(g ° f)(b) is equal to ____.

For some $\displaystyle a, b, c \in \mathbb{N}$, let $\displaystyle f(x)=a x-3$ and $\displaystyle g(x)=x^b+c, x \in \mathbb{R}$. If $\displaystyle (f \circ g)^{-1}(x)=\left(\frac{x-7}{2}\right)^{1 / 3}$, then $\displaystyle (f \circ g)(a c)+(g \circ f)(b)$ is equal to $\displaystyle \_\_\_\_$.
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.