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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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