AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are defined by \(f(x)=|x|\) and \(g(x)=[x-3]\) for \(x \in R\), then \(\left\{g(f(x)):-\frac{8}{5} < x < \frac{8}{5}\right\}\) is equal to
- A \(\{0,1\}\)
- B \(\{1,2\}\)
- C \(\{-3,-2\}\)
- D \(\{2,3\}\)
Answer & Solution
Correct Answer
(C) \(\{-3,-2\}\)
Step-by-step Solution
Detailed explanation
Given that, \(f(x)=|x|\) and \(g(x)=[x-3]\) For \(\quad-\frac{8}{5} < x < \frac{8}{5}, 0 \leq f(x) < \frac{8}{5}\) Now, for \(\quad 0 \leq f(x) < 1\), \[ \begin{aligned} g(f(x)) & =[f(x)-3] \\ & =-3[\because-3 \leq f(x)-3 < -2] \end{aligned} \] Again, for \(1 \leq f(x) < 1.6\)…
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