FONER
The function f: R + R, f\x) = 5x + 7 then the function | is
TA One one and onto
TÉT One ne and not onto
o Onto but not one one
D. Neither one one nor onto
Answers
Answer :
A. One-one and Onto
Solution :
Given function :
f : R → R , f(x) = 5x + 7
• Whether f(x) is one-one :-
Let f(x1) = f(x2)
=> 5x1 + 7 = 5x2 + 7
=> 5x1 = 5x2
=> x1 = x2
Since f(x1) = f(x2) => x1 = x2 , hence f(x) is one-one function .
• Whether f(x) is onto :-
Let y = f(x)
=> y = 5x + 7
=> 5x = y - 7
=> x = (y - 7)/5
Since the domain of the function is R , thus for x to be real y can be any real number .
=> Range (f) = R
=> Range (f) = Co-domain (f)
Since the range and the Co-domain of the given function are equal , hence f(x) is onto function .
Hence ,
f(x) is one-one and onto function .
Answer:
f(x)=x−5[
5
x
]
Take x in intervals of 5 natural numbers
f(x)=
⎩
x−5(0)
x−5(1)
x−5(2)
x−5(3)
0≤x<5
5≤x<10
10≤x<15
15≤x<20
x∈N.
From graph, we can see that f(x) is neither one-one nor onto (as it does not take all N).
Step-by-step explanation:
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