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Answer :
The value of fog= gof is x² - 5x = 0
What are functions?
Functions are rules or expressions showing the relationship between an independent and dependent variable.
Given the functions:
- f(x) = x/ x+ 3
- g(x) = x - 2
fog(x) and gof(x) are both known as composite functions
If fog(x) = gof(x)
Then , we have
[tex]\frac{x - 2}{x -2 + 3} = \frac{x}{x + 3} -2[/tex]
solve the fractions
[tex]\frac{x-2}{x -1} = \frac{2x - 2x +6}{x+3}[/tex]
[tex]\frac{x -2}{x -1} = \frac{6}{x + 3}[/tex]
cross multiply
(x -2) ( x+ 3) = 6 ( x -1)
expand the bracket
x²+ 3x - 2x - 6 = 6x - 6
collect like terms
x² - 5x + 0 = 0
x² - 5x = 0
Thus, the value of fog= gof is x² - 5x = 0
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