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प्रश्न
Let f: R → R be defined by f(x) = `x/sqrt(1 + x^2)`. Then (f o f o f) (x) = ______.
रिकाम्या जागा भरा
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उत्तर
Let f: R → R be defined by f(x) = `x/sqrt(1 + x^2)`. Then (f o f o f) (x) = `x/sqrt(1 + 3x^2)`.
Explanation:
Given that, f(x) = `x/sqrt(1 + x^2)`
∴ (fofof)(x) = f[f(f(x))]
= `f[f(x/sqrt(1 + x^2))]`
= `f((x/sqrt(1 + x^2))/sqrt(1 + x^2/(1 + x^2)))`
= `f(x/sqrt(1 + 2x^2))`
= `(x/sqrt(1 + 2x^2))/sqrt(1 + x^2/(1 + 2x^2))`
= `x/sqrt(1 + 3x^2)`
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Inverse of a Function
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