Question

Question 25.Show if given 1-1 functions are inverse of each other. Graph both functions on the same set of axes and show the line Y=x as a dotted line on graph.

Answer 1

Given:

$\begin{gathered} f(x)=3x+1_{} \\ g(x)=\frac{x-1}{3} \end{gathered}$

To check the given functions are inverses of each other,

$\begin{gathered} To\text{ prove: }f\mleft(g\mleft(x\mright)\mright)=x\text{ and g(f(x)=x} \\ f(g(x))=f(\frac{x-1}{3}) \\ =3(\frac{x-1}{3})+1 \\ =x-1+1 \\ =x \end{gathered}$

And,

$\begin{gathered} g(f(x))=g(3x+1) \\ =\frac{(3x+1)-1}{3} \\ =\frac{3x+1-1}{3} \\ =\frac{3x}{3} \\ =x \end{gathered}$

It shows that, the given functions are inverses of each other.

The graph of the function is,

Blue line represents g(x)

Red line represents f(x)

green line represents y=x