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Question
Answer the following:
Find (f ° f) (x) if f(x) = `x/sqrt(1 + x^2)`
Solution
f(x) = `x/sqrt(1 + x^2)`
∴ (f ° f) (x) = f[f(x)]
= `"f"[x/sqrt(1 + x^2)]`
= `((x/sqrt(1 + x^2)))/(sqrt(1 + (x/sqrt(1 + x^2))^2`
= `((x/sqrt(1 + x^2)))/(sqrt(1 + x^2/(1 + x^2))`
= `((x/sqrt(1 + x^2)))/(sqrt((1 + x^2 + x^2)/(1 + x^2)`
= `x/sqrt(1 + 2x^2)`
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