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suppose that the functions f and g are defined for all real numbers x as follows.
f(x)=x-5
g(x)=4x+1
write the expression for (f+g)(x) and (f*g)(x) and evaluate (f-g)(3)
(f+g)(x)=?
(f*g)(x)=?
(f-g)(3)=?

Respuesta :

Answer:

(f+g)(x)=5x-4

(f*g)(x)=(4x^2-19x-5)

(f-g)(3)=(-15)

Step-by-step explanation:

(f+g)(x)=(x-5)+(4x+1)=(5x-4)

(f*g)(x)=(x-5)(4x-1)=(4x^2-19x-5)

(f-g)(3)=(x-5)-(4x-1)=(3-5)-(4(3)+1)=(-2)-(12+1)=(-2)-(13)=-15 substitute 3 for x

Given:

Two functions 'f' and 'g' as,

f(x) = x - 5

g(x) = 4x + 1

To Find:

Composite functions,

(f + g)(x)

(f * g)(x)

(f - g)(x)

Solution:

Given functions are,

f(x) = x - 5

g(x) = 4x + 1

Expression for the composite functions will be,

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

              = (x - 5) + (4x + 1)

              = 5x - 4

(f * g)(x) = f(x) × g(x)

             = (x - 5)(4x + 1) [By distribution property]

             = x(4x + 1) - 5(4x + 1)

             = 4x² + x - 20x - 5

             = 4x² - 19x - 5

(f - g)(x) = f(x) - g(x)

             = (x - 5) - (4x + 1)

             = x - 4x - 5 - 1

             = -3x - 6

Therefore, (f - g)(3) = -3(3) - 6

                                = -9 - 6

                                = -15

Learn more about the composite functions from,

https://brainly.com/question/3386591

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