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Find the component g.

Given the function
f(x)= x - 2
-------
5
gf(x) = x - 3

How to solve this question? Can you show me how to do it step by step?

Respuesta :

Answer:

The function [tex]g(x) = x-1[/tex]

Step-by-step explanation:

Here [tex]f(x) = x-2[/tex]

Let [tex]y=x-2[/tex]

Solving for x we get

[tex]x=y+2[/tex]    ....(1)

We are also given that

[tex]g(f(x)) = x-3[/tex]

So we replace [tex]f(x) \ by \ y[/tex]

We get

[tex]g(y) = x-3[/tex]

But [tex]x=y+2 \ from \ (1)[/tex]

We have

[tex]g(y) = y+2-3[/tex]

[tex]g(y)=y-1[/tex]

or

[tex]g(x)=x-1[/tex]

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