Functions

Determine whether the given mapping is a real function or not.

Let $f:R\to [0,\infty )$ defined by $f\left(x\right)=x^2$ for all $x\in R$.

Define bounded function and find the bounded values of $y=\sin x+\cos x$.

Define bounded function and find the bounded values of $y=\cos 2x$.

Define bounded function and find the bounded values of $y=\sin 2x$.

Define bounded function and find the bounded values of $y=\cos x$.

Define bounded function and find the bounded values of $y=\sin x$.

Are $f\left(x\right)=x^2$ and $g\left(x\right)=x^3$ are equal functions? Find the values of $f\left(4\right)$ and $g\left(4\right)$.

Are $f\left(x\right)=3x^2$ and $g\left(x\right)=3x^3$ are equal functions? Find the values of $f\left(3\right)$ and $g\left(3\right)$.

Are $f\left(x\right)=2x^2$ and $g\left(x\right)=2x^3$ are equal functions? Find the values of $f\left(2\right)$ and $g\left(2\right)$.

Are $f\left(x\right)=x^2$ and $g\left(x\right)=x^3$ are equal functions? Find the values of $f\left(3\right)$ and $g\left(3\right)$.

Are $f\left(x\right)=x^2$ and $g\left(x\right)=x^3$ are equal functions? Find the values of $f\left(2\right)$ and $g\left(2\right)$.

If $f$ and $g$are real functions defined by $f\left(x\right)=x+7$ and $g\left(x\right)=3x+5$, then find the value of $f\left(3\right)-g\left(2\right)$.

If $f\left(x\right)=\frac{1}{x^2 + 4x + 4}-\frac{4}{x^4 + 4x^3 + 4x^2}+\frac{4}{x^3 + 2x^2},$ then $f\left(\frac{1}{2}\right)$ is equal to

A function $\text{'}f\text{'}$ is defined by $f\left(x\right)=x-1$, where $x\in \{0,3,5\}$. Then find its co-domain.

If $X=\{0,1,2,3\} \text{and} Y=\{a,b,c\}$, check the relation $R=\left\{\right(0,a),(1,a),(2,b\left)\right\}$ is a function from $X\hspace{0.17em}\text{to} Y$. If so find its co-domain.

If $y=3+\sin x$ then $y$ is bounded between $-3$ and $3$

If $y=3\sin x$ then $y$ is bounded between $-3$ and $3$

Examine whether the following pair of functions are identical or not, $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sgn}\left(x\right)$ and $\mathrm{g}\left(\mathrm{x}\right)=\left\{\begin{array}{c}\frac{\mathrm{x}}{\left|\mathrm{x}\right|} x\ne 0\\ 0 x=0\end{array}\right.$.

If$f\left(x\right)=\cos (\log x)$, then the value of $f\left(x\right).f\left(y\right) –\frac{1}{2}\left[ f\left(\frac{x}{y}\right) + f(x.y)\right]$ is

If $f\left(x\right)=\frac{ x}{1–x}=\frac{1}{y}$, then the value of $f\left(y\right)$ is