For the given curve y = x³ given in figure draw, try to draw with the same scale
(i) y = -x³ 
(ii) y = x³+1
(iii) y = x³-1
(iv) y = (x + 1)³

For the given curve, \(y=x^{1\over 3}\)given in  figure draw
(i) \(y=-x^{ \left( \frac { 1 }{ 3 } \right) }\)
(ii) ​\(y=x^{ \left( \frac { 1 }{ 3 } \right) }+1\)
(iii)​ \(y=x^{ \left( \frac { 1 }{ 3 } \right) }-1\)
(iii) ​\(y=(x+1)^{1\over 3}\)​

From the curve y = x, draw
(i) y = - x
(ii) y = 2x
(iii) y = x + 1
(iv) ​\(y={1\over 2}x+1\)​
(v) 2x + y + 3 = 0

Write the values of f at -3, 5, 2, -1, 0 if
\(f(x)=\begin{cases} x^2+x-5\quad if\ x \in(-\infty, 0) \\x^2+3x-2\quad if\ x\in(3,\infty) \\x^2\quad \quad \quad \quad \quad if\ x\ \in(0,2) \\x^2-3 \quad \quad \quad otherwise \end{cases}\)

Find the range of the function \(\frac { 1 }{ 2cosx-1 } \)

Check the following functions for one-to-oneness and ontoness.
(i) \(f:N\rightarrow N\) defined by f(n) = n².
(ii) \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by f(n) = n².

Find the largest possible domain for the real valued function given by \(f(x)={\sqrt{9-x^2}\over{x^2-1}}.\)

Let f, g: \(R \rightarrow R\) be defined as f (x) = 2x -|x| and g(x) = 2x + |x|. find f o g.

If \(f:R\rightarrow R\)  is defined by f(x) = 2x- 3, prove that f is a bijection and find its inverse