Let f : R R be any function. Define g : R R by g ( x ) = | f ( x ) | for all x . Then g is [2000]

Question

Let $f : R \to R$ be any function. Define $g : R \to R$ by $g (x) =$ $| f (x) |$ for all $x$ . Then $g$ is [2000]

Smart Achievers · Accepted Answer

(3)

$Let h (x) =$ $| x |$

$∴$ $g (x) =$ $| f (x) |$ $= h (f (x))$

Since the composition of two continuous functions is continuous, therefore $g$ is continuous if $f$ is continuous.

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