If f : R → R be defined as f(x) = 𝑥4,then the function f isa) one-one and onto b) many-oneandontoc) one-one but not onto d ) neither one-one nor ont
Question
If f : R → R be defined as
f(x) = 𝑥^4, then the function f is
a) one-one and onto
b) many-one and onto
c) one-one but not onto
d) neither one-one nor onto
Solution
The function f(x) = x^4 is a many-one function, not a one-one function. This is because for any given y in the range, there are multiple x values (specifically, one positive and one negative) that satisfy the equation y = x^4.
The function is also not onto. This is because the range of f(x) = x^4 is the set of all non-negative real numbers, not the set of all real numbers. There are real numbers (specifically, any negative number) that cannot be obtained by squaring a real number.
So, the correct answer is: the function f is many-one but not onto.
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