Let f-R- R be a function- Define g-R- R by g x - - f x - for all x- Then g is

The correct option is C continuous if f is continuous g( x ) =| f( x ) #160; | Let h( f( x ) #160; ) =g( x ) Where h( x ) =| x | We kno ...

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Standard XII

Mathematics

Derivative of Standard Functions

Let f:R→ R ...

Question

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

onto if

f

is onto

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one-to-one if

f

is one-to-one

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continuous if

f

is continuous

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differentiable if

f

is differentiable

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Solution

The correct option is C continuous if $f$ is continuous
$g (x) = | f (x) |$
Let $h (f (x)) = g (x)$
Where $h (x) = | x |$
We know that $| x |$ is continuous everywhere
$∴$ if f is continuous
Then $h (f (x))$ is continuous
$g (x)$ is continuous.

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Let f:R→R be a function. Define g:R→R by g(x)=|f(x)| for all x. Then g is

The correct option is C continuous if f is continuousg(x)=|f(x)|Let h(f(x))=g(x)Where h(x)=|x|We know that |x| is continuous everywhere∴ if f is continuousThen h(f(x)) is continuous g(x) is continuous.

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

The correct option is C continuous if $f$ is continuous
$g (x) = | f (x) |$
Let $h (f (x)) = g (x)$
Where $h (x) = | x |$
We know that $| x |$ is continuous everywhere
$∴$ if f is continuous
Then $h (f (x))$ is continuous
$g (x)$ is continuous.