Question

A function f: R –{0} " R define by f(x) = 1/x is called a
(a) cubic function
(b) reciprocal function
(c) constant
(d) none of these

Answer 1

(b) Reciprocal function

The real function $\displaystyle\sf{f:\mathbb{R}-\{0\}\to\mathbb{R}}$ defined by $\displaystyle\sf{f(x)=\dfrac{1}{x}}$ is known as reciprocal function and the graph appears as a hyperbola with axes as the asymptotes.

The domain of $\displaystyle\sf{f}$ is $\displaystyle\sf{\mathbb{R}-\{0\}}$ and the range is also $\displaystyle\sf{\mathbb{R}-\{0\}.}$

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(a) The real function $\displaystyle\sf{f:\mathbb{R}\to\mathbb{R}}$ defined by $\displaystyle\sf{f(x)=ax^3+bx^2+cx+d}$ for some real numbers $\displaystyle\sf{a,\ b,\ c,\ d}$ but $\displaystyle\sf{a\neq0}$ is called a cubic function and it's graph is a curve having two distinct vertices. It's domain as well as range is $\displaystyle\sf{\mathbb{R}.}$

(c) The real function $\displaystyle\sf{f:\mathbb{R}\to\mathbb{R}}$ defined by $\displaystyle\sf{f(x)=c}$ for some constant $\displaystyle\sf{c}$ is called a constant function and the graph of this function shows a straight line parallel to the x axis. It's domain is $\displaystyle\sf{\mathbb{R}}$ and range is $\displaystyle\sf{\{c\}.}$