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Composite functions are functions derived from combining other functions
The values of the composite functions are [tex](f + g)(2) = -3[/tex] and [tex](f - g)(2) = 41[/tex]
The single functions are given as:
[tex]f(x) =11 + 2x^2[/tex]
[tex]g(x) = -7x - 3x^2 + 4[/tex]
To calculate (f + g)(x), we make use of
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 11 + 2x^2 - 7x - 3x^2 + 4[/tex]
Collect the like terms
[tex](f + g)(x) = 2x^2- 3x^2 - 7x + 4+11[/tex]
Evaluate
[tex](f + g)(x) = - x^2 - 7x + 15[/tex]
Substitute 2 for x
[tex](f + g)(2) = - 2^2 - 7(2) + 15[/tex]
[tex](f + g)(2) = -3[/tex]
To calculate (f - g)(x), we make use of
[tex](f + g)(x) = f(x) - g(x)[/tex]
So, we have:
[tex](f - g)(x) = 11 + 2x^2 + 7x + 3x^2 - 4[/tex]
Collect the like terms
[tex](f - g)(x) = 2x^2 + 3x^2+ 7x - 4 + 11[/tex]
Evaluate
[tex](f - g)(x) = 5x^2+ 7x +7[/tex]
Substitute 2 for x
[tex](f - g)(2) = 5 * 2^2+ 7* 2 +7[/tex]
[tex](f - g)(2) = 41[/tex]
Hence, the values of the composite functions are [tex](f + g)(2) = -3[/tex] and [tex](f - g)(2) = 41[/tex]
Read more about composite functions at:
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The value of f(x) - g(x) and f(x) + g(x) are 52 and 0
Given the following function expressed as:
f(x) = 11x + 2x^2 and;
g (x) = -7x - 3x^2 + 4
Taking the sum of the function
f(x) + g(x) = 11x + 2x^2 -7x - 3x^2 + 4
f(x) + g(x) = -x^2 + 4x + 4
If x = 2,
f(x) + g(x) = -4 + 8 + 4
f(x) + g(x) = 0
For the difference;
f(x) - g(x) = 11x + 2x^2 + 7x + 3x^2 - 4
f(x) - g(x) = 5x^2 + 18x - 4
If x = 2,
f(x) - g(x) = 5(4) + 36 - 4
f(x) - g(x) = 52
Hence the value of f(x) - g(x) and f(x) + g(x) are 52 and 0
Learn more on sum of function here: https://brainly.com/question/17431959