JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f: R \rightarrow R\) be defined as \(f(x)=x-1\) and \(g: R -\{1,-1\} \rightarrow R\) be defined as \(g(x)=\frac{x^{2}}{x^{2}-1}\). Then the function fog is
- A one-one but not onto function
- B onto but not one-one function
- C both one-one and onto function
- D neither one-one nor onto function
Answer & Solution
Correct Answer
(D) neither one-one nor onto function
Step-by-step Solution
Detailed explanation
\(f ( x )= x -1 ; g ( x )=\frac{x^{2}}{x^{2}-1}\) \(f ( g ( x ))= g ( x )-1\) \(\quad=\frac{ x ^{2}}{ x ^{2}-1}-1=\frac{ x ^{2}- x ^{2}+1}{ x ^{2}-1}\) \(f ( g ( x ))=\frac{1}{x^{2}-1} ; x \neq \pm 1 \text {, even function }\) \(\rightarrow\) Hence \(f ( g ( x ))\) is many one…
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