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If the function be defined as and be defined as , show that .

Mathematics20204 marksDerivation
If the function $f : \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = \frac{3x + 4}{5x - 7}, x \ne \frac{7}{5}$ and $g : \mathbb{R} \to \mathbb{R}$ be defined as $g(x) = \frac{7x + 4}{5x - 3}, x \ne \frac{3}{5}$, show that $(g \circ f)(x) = (f \circ g)(x)$.

Given: $f(x) = \frac{3x + 4}{5x - 7}, x \ne \frac{7}{5}$ and $g(x) = \frac{7x + 4}{5x - 3}, x \ne \frac{3}{5}$

To show: $(g \circ f)(x) = (f \circ g)(x)$

Answer

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Relations and Functions

From ISC 2020 Mathematics Paper 1, question 2.