Math, asked by deva1012, 10 months ago

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Answered by pranjaygupta
0

Answer:

bijective, not bijective

Step-by-step explanation:

bijective means both one one and onto

for checking if the function is one one or many one

find f'(x) , if f'(x) is positive or negative for all real x then the function is one one otherwise many one

for checking if the function is onto or into

onto function have their range = codomain

so just find the range and check if it's equal to the codomain or not

if equal onto otherwise into

(i) f(x)= 2x+1

f'(x) = 2>0 for all real x

therefore one one

range is -infinty to +infinity therefore range is equal to codomain

hence onto

thus bijective

(ii) f(x)= 3-4x^2

f'(x)= -8x not throughout positive or negative for all real x

thus into

here we can conclude the function is not bijective no need to find onto or into

but still let's find

range = -D/4a ( for any quadratic equation)

-(-4(-4)(3))/4(-4)

-48/-16

48/16

3

therefore range is (-infinty ,3) ......as a is negative

it's not equal to codomain hence into

hope it helps u

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