Find f(x+2) for the following function: f(x)= sqrt((x-5)^2 +4

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to substitute x+2 for x in the equation of f(x) such that:

`f(x+2) = sqrt((x+2-5)^2+4)`

Computing the difference of like terms in brackets yields:

`f(x+2) = sqrt((x-3)^2+4)`

Expanding the binomial yields:

`f(x+2) = sqrt(x^2 - 6x + 9 + 4)=gt f(x+2) = sqrt(x^2 - 6x + 13)`

Notice that you need to use the next formula to raise the binomial `(x-3)^2`  to square:

`(a-b)^2 = a^2 - 2ab + b^2`

Hence, evaluating the function at x + 2 yields `f(x+2) = sqrt(x^2 - 6x + 13).`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function `f(x) = sqrt((x - 5)^2 + 4)`

The expression for f(x+2) has to be found. Replace x with (x + 2) in f(x)

=> f(x+2) = `sqrt((x+2-5)^2+4)`

=> `sqrt((x-3)^2+4)`

=> `sqrt(x^2+9-6x+4)`

=> `sqrt(x^2-6x+13)`

The expression for `f(x+2) = sqrt(x^2-6x+13)`

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