Let f - R - R be a function- Define g - R - by g x - f x - for all x- Then g isA- Onto if f is ontoB- One-one if f is one-oneC- Continuous if f is continuousD- None of these

The correct option is C Continuous if f is continuousg(x)=|f(x)|≥ 0. So g(x) cannot be onto. if f(x) one one and f(x_1)= f(x_2) then g(x_1)=g(x_2). So, 'f(x) ...

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Byju's Answer

Standard XI

Mathematics

Graphical Interpretation of Continuity

Let f : R → R...

Question

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

Onto if f is onto

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One-one if f is one-one

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Continuous if f is continuous

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None of these

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Solution

The correct option is C Continuous if f is continuous
$g (x) = | f (x) | \geq 0. S o g (x)$ cannot be onto. if f(x) one-one and $f (x_{1}) = - f (x_{2})$ then
$g (x_{1}) = g (x_{2})$ .
So, 'f(x) is one-one' does not ensure that g(x) is one-one.

If f(x) is continuous for $x \in R, (x)$ is also continuous for $x \in R$ .
This is obvious from the following graphical consideration.
So g is continuous if f is continuous.

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

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