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NVAMediumJEE Main 2023 · 30 January, Shift 1Composition & Inverse Functions

Mathematics Question from JEE Main 2023 · 30 January, Shift 1

Let f1(x)=3x+22x+3,x∈R,R−(−32).f^1(x) = \frac{3x + 2}{2x + 3}, \quad x \in \mathbb{R}, \quad R - \left( -\frac{3}{2} \right). For n≥2n \geq 2, define fn(x)=f1∘fn−1(x)f^n(x) = f^1 \circ f^{n-1}(x) and if

f5(x)=ax+bbx+a,gcd⁡(a,b)=1,thena+b is equal to:f^5(x) = \frac{ax + b}{bx + a}, \quad \gcd(a, b) = 1, \quad \text{then} \quad a + b \text{ is equal to:}

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