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Question

# Let f:R→R be a function such that for any irrational number r, and any real number x we have f(x)=f(x+r). Then, f is

A
an identity function
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B
a constant function
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C
a zero function
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D
onto function
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Solution

## The correct option is A a constant functionA constant function is a function that has the same output value no matter what your input value is. Because of this, a constant function has the form y=k where k is a constant(a single value that doesn't change).So in here our input is x i f we change our input to say x+rand still output does'nt change i.e.f(x)=f(x+r)it means it is a constant function,example:f(x)=5=5(x)0f(x+r)=5(x+r)0f(x+r)=5×1f(x+r)=5=f(x)

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