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)=(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((x-1)/(3)) \\ =3((x-1)/(3))+1 \\ =x-1+1 \\ =x \end{gathered}`

And,

`\begin{gathered} g(f(x))=g(3x+1) \\ =((3x+1)-1)/(3) \\ =(3x+1-1)/(3) \\ =(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