Question

In two or more complete sentences, explain how to use ordered pairs of points in x) = 2x + 5 and g(x)=

to
determine if Ax) and g(x) are inverses of each other

Answer 1

see the explanation

Explanation:

we have

`A(x)=2x+5`

Find the inverse of A(x)

Let

y=A(x)

`y=2x+5`

Exchange the variables x for y and y for x

`x=2y+5`

Isolate the variable y

`2y=x-5`

`y=(x-5)/(2)`

Let

`g(x)=y`

`g(x)=(x-5)/(2)` ------> function inverse of A(x)

Explanation

For x=1

Find the value of A(x)

`A(1)=2(1)+5=7`

The point (1,7) is a solution for A(x)

That means-----> The point (7,1) is a solution for the function inverse g(x)

Verify

For x=7

`g(7)=(7-5)/(2)=1`

The point (7,1) is a solution for g(x)

therefore

A(x) and g(x) are inverses of each other if the point (x,y) is a solution of A(x) and the point (y,x) is a solution of g(x)