Relations and F...

If \(f(x)=x^{4}-\frac{1}{x^{4}}\), then \(f(x)+f\left(\frac{1}{x}\right)=?\)

The 2 functions in \(x\) are \(f(x)=e^{2 x}\) and \(g(x)=\ln x\), then find \(\operatorname{gof}(x)\)?

In the set of real numbers \(\mathrm{R}\), an operation * is defined by \(\mathrm{a} * \mathrm{b}=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}\). Then, value of \(\left(3 {*} 4\right) \times 5\):

Let, \(R=\{(a, b): a, b \in Z\) and \((a+b)\) is even \(\}\), then \(R\) is:

If \(f(x)=\frac{x+1}{x-1}, x \neq 1\), then \(f\{f(x)\}=?\)

If \({ }^{*}\) is a binary operation on \(\mathrm{Z}\) such that \(\mathrm{a}^{*} \mathrm{~b}=\mathrm{a}+\mathrm{b}+1 \forall \mathrm{a}, \mathrm{b} \in \mathrm{Z}\) then find the identity element of \(\mathrm{Z}\) with respect to \({ }^{\star}\)?

If the function is onto and one-to-one, then it is called as ________.

If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are two mappings defined as \(f(x)=3 x\) and \(g(x)=3 x^{2}+9\), then the value of \((f+g)(2)\) is:

Let \(R\) be a relation defined as \(R=\left\{(a, b): a^{2} \geq b\right.\), where \(a\) and \(b \in Z\}\). Then, relation \(R\) is a/an:

What is the inverse of the function \(y=5^{\log x}\)?