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Let f(x) = 11x + 2x^2 and g (x) = -7x - 3x^2 + 4 . Find (f + g) (x) and (f - g) (x) . Then evaluate f + g and f - g for x = 2

Sagot :

MrRoyal

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]

How to determine the composite functions

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:

https://brainly.com/question/10687170

abidemiokin

The value of f(x) - g(x) and f(x) + g(x) are 52 and 0

Sum and differences of function

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

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