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Let f(x) = 3x^(2) + 6x + 5 and g(x) = x ...

Let f(x) `= 3x^(2) + 6x + 5` and g(x) = x + 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and `((f)/(g))(x)`

Text Solution

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Given that
`f(x) = 3x^(2) + 6x + 5`
`g(x) = x+1`
Now, `(f+g)(x) = f(x) + g(x)`
`= 3x^(2) + 6x + 5 + x+1`
`= 3x^(2) + 7x + 6`
(f-g)(x) = f(x) - g(x)
`= 3x^(2) + 6x + 5 - x - 1`
`= 3x^(2) + 5x + 4`
`(fg)(x) = f(x)g(x) = (3x^(2) + 6x + 5)(x+1)`
`= 3x^(2) + 3x^(2) + 6x^(2) + 6x + 5x + 5`
`((f)/(g))(x) = (f(x))/(g(x)) = (3x^(2) + 6x + 5)/(x+1), x != -1`
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