AP EAMCET · Maths · Functions
Which of the following is false?
- A If \(f\) is an even function from \(R\) to \(R\), then \(f(0)\) must be equal to 0 .
- B \(f: R \rightarrow R\) defined by \(f(x)=x-[x], \forall x \in R\), where \([x]\) is the greatest integer not greater than \(x\), is a periodic function
- C If \(f: R \rightarrow R\) is an odd function, then \(f(0)=0\)
- D Number of onto functions from \(\{1,2,3,4,5,6\}\) to \(\{1,2\}\) is 62
Answer & Solution
Correct Answer
(A) If \(f\) is an even function from \(R\) to \(R\), then \(f(0)\) must be equal to 0 .
Step-by-step Solution
Detailed explanation
(a) If \(f\) is an even function from \(R\) to \(R\), then \(f(0)\) must be equal to 0 . \(\because\) We know that if a function \(f(x)\) is even, then \(f(-x)=f(x)\) Now, if we assume \(f(x)=\cos x\)…
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