Invertible Functions

Consider the function $f\left(x\right)=\frac{1}{x+2}$, then $f\left(x\right)$ is 

Consider the function $f\left(x\right)=\frac{1-2x}{3x+6}$, $x\ne -2, x\in R$, then $f$ is

Consider the function $f\left(x\right)=\frac{1-2x}{3x+6}$, $x\ne -2, x\in R$, If the inverse function $f^{-1}\left(x\right)$ is $R-\left\{k\right\}$, then the value of $k$ is

Consider the function $f\left(x\right)=\frac{1-2x}{3x+6}$, $x\ne -2, x\in R$, If the domain of $f^{-1}\left(x\right)$ is $R-\left\{-k\right\}$, then the value of $k$ is

Consider the function $f\left(x\right)=\frac{1}{x+2}$, then $f\text{'}\left(x\right)$ is 

The function $f\left(x\right)$ is defined as such that $f\left(x\right)=x^2-6x+13$, $x\in R$, then interval in which $f\left(x\right)$ is increasing is

The function $f\left(x\right)$ is one-to-one and defined such that $f\left(x\right)=x^2-6x+13$, $x\in R$, then $f\text{'}\left(x\right)$ at $x=9$ is

The function $f\left(x\right)$ is one-to-one and defined such that $f\left(x\right)=x^2-6x+13$, $x\ge k,x\in R,k\in R$. Find the least possible value for $k$.

Any linear function has an inverse function.

A many-to-one function does not have an inverse function.

Find the formula for the given function. Further, explain why it has an inverse function and hence find the formula of its inverse function.

The volume of a certain type of wood in terms of the weight: 

Find the formula for the given function. Further, explain why it has an inverse function and hence find the formula of its inverse function.

The price $P$ you pay in Happy Shop in terms of the regular price $R$ if there is a sign that says "Today you pay $15\%$ less for every single item".

Find the formula for the given function. Further, explain why it has an inverse function and hence find the formula of its inverse function.

The number of pounds in weight, $p$, relating to a weight in kilograms, $k$. Note that $1$kg is equivalent to $2.2$ pounds.

The diagram shows the graph of a function $f$ from $A$ to $B$.

Find $f^{-1}\left(-1\right)$.

The diagram shows the graph of a function $f$ from $A$ to $B$.

Find $f^{-1}\left(1\right)$.

Describe the difference between a linear function that has an inverse and one that does not.

Describe the difference between a linear function that has an inverse and one that does not.

Describe the difference between a linear function that has an inverse and one that does not.

Describe the difference between a linear function that has an inverse and one that does not.