Let f - B - C and g- A - B be two functions and let h - f - g- Given that h is an onto function- Which one of the following is TRUE -

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Standard X

Mathematics

Into Function

Let f : B → C...

Question

Let $f : B \to C$ and $g : A \to B$ be two functions and let $h = f \circ g$ , Given that $h$ is an onto function. Which one of the following is TRUE ?

f

and

g

should both be onto functions

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f

should be onto but

g

need not be onto

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g

should be onto but

f

not be onto

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Both

f

and

g

need not be onto

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Solution

The correct option is B $f$ should be onto but $g$ need not be onto
Consider the arrow diagram shown below:

Here $f$ is onto but $g$ is not onto, yet $h$ is onto.
As can be seen from diagram if $f$ is not onto, $h$ cannot be onto.
$∴ f$ should be onto, but $g$ need not be onto.
$∴$ Answer is (b)

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Let f:B→C and g:A→B be two functions and let h=f∘g, Given that h is an onto function. Which one of the following is TRUE ?

The correct option is B f should be onto but g need not be ontoConsider the arrow diagram shown below: Here f is onto but g is not onto, yet h is onto. As can be seen from diagram if f is not onto, h cannot be onto. ∴f should be onto, but g need not be onto. ∴ Answer is (b)

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