TS EAMCET · Maths · Functions
If \(\quad f: Z \rightarrow Z \quad\) is \(\quad\) defined \(f(x)=\left\{\begin{array}{lll}\frac{x}{2}, & \text { if } & x \text { is even } \ 0, & \text { if } & x \text { is odd }\end{array}\right.\), then \(f\) is
- A onto but not one-to-one
- B one-to-one but not onto
- C one-to-one and onto
- D neither one-to-one nor onto
Answer & Solution
Correct Answer
(A) onto but not one-to-one
Step-by-step Solution
Detailed explanation
Given, \(f: Z \rightarrow Z, f(x)=\left\{\begin{array}{l}\frac{x}{2}, \text { if } x \text { is even } \\ 0, \text { if } x \text { is odd }\end{array}\right.\) when \(x\) is odd, \(f(1)=f(3)=0\) \(\Rightarrow f(x)\) is not one-one function. when \(x\) is even i.e.,…
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