AP EAMCET · Maths · Functions
Define the functions \(f, g\) and \(h\) from R to R such that \(f(x)=x^2-1, g(x)=\sqrt{x^2+1}\) and \(h(x)=\left\{\begin{array}{l}0, \text { if } x \leq 0 \\ x, \text { if } x \geq 0\end{array}\right.\)
consider the following statements
- A fog is invertible
- B \(h\) is an identify function
- C fog is not invertible
- D \((h \circ f \circ g) x=x^2\)
Answer & Solution
Correct Answer
(C) fog is not invertible
Step-by-step Solution
Detailed explanation
\(f \circ g(x)=f\left(\sqrt{x^2+1}\right)=\left(x^2+1\right)-1=x^2\) \(\because\) Codomain of \(\operatorname{fog}(x)=\mathrm{R}\) and Range of fog \((x)=[0, \infty)\) \(\therefore\) fog is not onto function \(\quad \Rightarrow\) fog is not invertible. Now…
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