Determine which of the following functions are self-inverse functions.

(b) $f\left(x\right)=\frac{2x+1}{x-2}$ for $x\in \mathrm{ℝ},x\ne 2$.

Determine which of the following functions are self-inverse functions.

(c) $f\left(x\right)=\frac{3x+5}{4x-3}$ for $x\in \mathrm{ℝ},x\ne \frac{3}{4}$

$f:x\mapsto 3x-5$ for $x\in \mathrm{ℝ} g:x\mapsto 4-2x$ for $x\in \mathrm{ℝ}$

(a) Find an expression for $\left(\mathrm{fg}{)}^{-1}\right(x)$.

$f:x\mapsto 3x-5$ for $x\in \mathrm{ℝ} g:x\mapsto 4-2x$ for $x\in \mathrm{ℝ}$

(b) Find expressions for:

(i) $f^{-1}{g}^{-1}\left(x\right)$

$f:x\mapsto 3x-5$ for $x\in \mathrm{ℝ} g:x\mapsto 4-2x$ for $x\in \mathrm{ℝ}$

(b) Find expressions for:

(i) $f^{-1}{g}^{-1}\left(x\right)$

$f:x\mapsto 3x-5$ for $x\in \mathrm{ℝ} g:x\mapsto 4-2x$ for $x\in \mathrm{ℝ}$

(c) Comment on your results in part b. Investigate if this is true for other functions.

On a copy of each grid, draw the graph of $f^{-1}\left(x\right)$ if it exists.

(a) 

Given f(x), draw the graph of $f^{-1}\left(x\right)$ if it exists.

(b) 

On a copy of each grid, draw the graph of $f^{-1}\left(x\right)$ if it exists..

(c)