Find inverse function of the following functions f(x) = 3x + 1, g(x) = x + 2 and find (f-g)(x) and (f-g)(5)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should use the following algorithm to find the inverses of the given functions, `f(x)`  and `g(x), ` such that:

`y = 3x + 1 => y - 1 = 3x => x = y/3 - 1/3`

`y = x + 2 => x = y - 2`

Hence, evaluating the inverses of the givn functions yields `f^(-1)(x) = x/3 - 1/3`  and `g^(-1)(x) = x - 2` .

You may evaluate `(f - g)(x)`  such that:

`(f - g)(x) = f(x) - g(x)`

`(f - g)(x) = 3x + 1 - (x + 2)`

`(f - g)(x) = 3x + 1 - x - 2 => (f - g)(x) = 2x - 1`

You may evaluate `(f - g)(5)`  substituting 5 for x in equation of `(f - g)(x)`  such that:

`(f - g)(5) = 2*5 - 1 = 9`

Hence, evaluating `f^(-1)(x), g^(-1)(x), (f - g)(x)`  and `(f - g)(5)`  yields `f^(-1)(x) = x/3 - 1/3, g^(-1)(x) = x - 2, (f - g)(x) = 2x - 1`  and `(f - g)(5) = 9` .

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x) = 3x + 1 and g(x) = x + 2.

f(x) = 3x + 1.

 `f(f^-1(x)) = x`

=> `3*f^-1(x) + 1 = x`

=> `f^-1(x) = (x - 1)/3`

The inverse function `f^-1(x) = (x - 1)/3`

 `g(x) = x + 2`

`g(g^-1(x)) = x`

=> `g^-1(x) + 2 = x`

=> `g^-1(x) = x - 2`

The inverse function `g^-1(x) = x - 2.`

 `(f - g)(x) = 3x + 1 - x - 2 = 2x - 1`

 `(f - g)(5) = 2*5 - 1 = 9`

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