Question

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

Answer 1

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: brainly.com/question/17431959

Answer 2

Composite functions are functions derived from combining other functions

The values of the composite functions are $(f + g)(2) = -3$ and $(f - g)(2) = 41$

How to determine the composite functions

The single functions are given as:

$f(x) =11 + 2x^2$

$g(x) = -7x - 3x^2 + 4$

To calculate (f + g)(x), we make use of

$(f + g)(x) = f(x) + g(x)$

So, we have:

$(f + g)(x) = 11 + 2x^2 - 7x - 3x^2 + 4$

Collect the like terms

$(f + g)(x) = 2x^2- 3x^2 - 7x + 4+11$

Evaluate

$(f + g)(x) = - x^2 - 7x + 15$

Substitute 2 for x

$(f + g)(2) = - 2^2 - 7(2) + 15$

$(f + g)(2) = -3$

To calculate (f - g)(x), we make use of

$(f + g)(x) = f(x) - g(x)$

So, we have:

$(f - g)(x) = 11 + 2x^2 + 7x + 3x^2 - 4$

Collect the like terms

$(f - g)(x) = 2x^2 + 3x^2+ 7x - 4 + 11$

Evaluate

$(f - g)(x) = 5x^2+ 7x +7$

Substitute 2 for x

$(f - g)(2) = 5 * 2^2+ 7* 2 +7$

$(f - g)(2) = 41$

Hence, the values of the composite functions are $(f + g)(2) = -3$ and $(f - g)(2) = 41$

Read more about composite functions at:

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