Answer:
see the explanation
Step-by-step explanation:
we have
[tex]A(x)=2x+5[/tex]
Find the inverse of A(x)
Let
y=A(x)
[tex]y=2x+5[/tex]
Exchange the variables x for y and y for x
[tex]x=2y+5[/tex]
Isolate the variable y
[tex]2y=x-5[/tex]
[tex]y=\frac{x-5}{2}[/tex]
Let
[tex]g(x)=y[/tex]
[tex]g(x)=\frac{x-5}{2}[/tex] ------> function inverse of A(x)
Explanation
For x=1
Find the value of A(x)
[tex]A(1)=2(1)+5=7[/tex]
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
[tex]g(7)=\frac{7-5}{2}=1[/tex]
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)
