Functions

Question

Comments

$(d)?$

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ans should be d

(a and b and c are one one since for every value we get a unique output.)

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Option A:

one-one and onto

Option B:

one - one and onto

Option C:

one - one and Not onto

Option D:

Not one - one And Not onto.

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Can you explain with an example pls

Answer 1

ans is d.

f(x)=x+5

f(x)= 3x-100

f(x)= $x^{3}$+1

put any int values like .....-3,-2,-1,0,1,2,3.... you will get unique values for f(x).

=> they are one one.

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for f(x)= $x^{2}$ +1

we can get same values for 2 and -2, 3 and -3 , 4 and -4 and so on for f(x)

$\Rightarrow$ so it is not one one.

It is also not onto since we will never be able to get a f(x)=0 for any value of  x. i.e. the range is not fully covered.