Respuesta :
You would do f(1)=2(1)=5, and g(1)=1-5/2. Then, you would compare the answers of both equations, after doing x=1, x=2, and x=3.
Answer:
f(x) and g(x) are inverse of each other.
Step-by-step explanation:
Given : Ordered pairs of points [tex]f(x)=2x+5[/tex] and [tex]g(x)=\frac{x-5}{2}[/tex]
To find : Determine if f(x) and g(x) are inverses of each other ?
Solution :
To determine f(x) and g(x) are inverse of each other then (fog)(x)=(gof)(x)
[tex]f(x)=2x+5[/tex] and [tex]g(x)=\frac{x-5}{2}[/tex]
LHS, [tex](fog)(x)=f(g(x))[/tex]
[tex](fog)(x)=f(\frac{x-5}{2})[/tex]
[tex](fog)(x)=2(\frac{x-5}{2}))+5[/tex]
[tex](fog)(x)=x-5+5[/tex]
[tex](fog)(x)=x[/tex]
RHS, [tex](gof)(x)=g(f(x))[/tex]
[tex](gof)(x)=g(2x+5)[/tex]
[tex](gof)(x)=\frac{(2x+5)-5}{2}[/tex]
[tex](gof)(x)=\frac{2x}{2}[/tex]
[tex](gof)(x)=x[/tex]
LHS=RHS
Therefore, f(x) and g(x) are inverse of each other.
