If f(x) = x-1x+1,x≠-1 Show that f(f(x)) = -1x, Provided x ≠ 0 - Mathematics

प्रश्न

If f(x) = $\frac{x - 1}{x + 1}, x \neq - 1$ Show that f(f(x)) = $- \frac{1}{x}$ , Provided x ≠ 0

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उत्तर

f(x) = $\frac{x - 1}{x + 1}, x \neq - 1$

= $[\frac{x - 1}{x + 1} - 1 \div \frac{x - 1}{x + 1} + 1]$

= $[\frac{x - 1 - (x + 1)}{x + 1} \div \frac{x - 1 + x + 1}{x + 1}]$

= $[\frac{x - 1 - x - 1}{x + 1}] \div \frac{2 x}{x + 1}$

= $\frac{- 2}{x + 1} \times \frac{(x + 1)}{2 x}$

= $- \frac{2}{2 x}$

= $- \frac{1}{x}$

f[f(x)] = $- \frac{1}{x}$

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Q 8 Q 7 Q 9. (i)

अध्याय 1: Relations and Functions - Unit Exercise – 1 [पृष्ठ ३४]

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सामाचीर कलवी Mathematics [English] Class 10 SSLC TN Board

अध्याय 1 Relations and Functions
Unit Exercise – 1 | Q 8 | पृष्ठ ३४

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If f(x) = x-1x+1,x≠-1 Show that f(f(x)) = -1x, Provided x ≠ 0 - Mathematics

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If f(x) = x-1x+1,x≠-1 Show that f(f(x)) = -1x, Provided x ≠ 0 - Mathematics

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