For the function f(x)=x2+​ 4 , solve for the whole number value of x when f(x) ​=40 .

The answer is:  " 6 " .
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     " x = 6 "  .
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Explanation:
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  Given:  " f(x) = x² + 4 " ;  Solve for the "whole number value of "x" ;
                                          when:  " f(x)= 40 " .
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 →  Rewrite the equation; by replacing:  " f(x)" with "40" ; 

 →  " 40 = x² + 4 "  ; 

 ↔  " x² + 4 = 40 " ;

Subtract "4" from EACH SIDE of the equation:

        x²  + 4 − 4  = 40 − 4  ; 

to get:
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→   x²  = 36 ; 

Now, take the "square root" of each side of the equation; 
        to isolate "x" on one side of the equation; & to solve for "x" ; 

→  √(x²)  =  √36 ; 

to get:

→  | x |  = 6 ; 

x = 6 ;  x = - 6 .

Note that:  "6" is a "whole number" .

Note that "negative numbers" are NOT "whole numbers" .

We are asked to find the "whole number value(s) for "x" ;
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The answer is:  " 6 " .
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     " x = 6 "  .
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