Question

f(x)=3x - 5
e. g(x)=-2x² - 5x
find (f - g)(x)

f(x)=3x³ - 3x
y. g(x)=x - 2
find (f + g)(x)

f(x)=-x - 4
w. g(x)=x³ - 3x
find (fg)(x)

f(x)=-4x - 5
m. g(x)=x³ - x - 4
find (f - g)(x)

Explanation:

E. Step1: Define $(f-g)(x)$

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

E. Step2: Substitute given functions

$(f-g)(x) = (3x - 5) - (-2x^2 - 5x)$

E. Step3: Simplify the expression

$(f-g)(x) = 3x - 5 + 2x^2 + 5x = 2x^2 + 8x - 5$

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Y. Step1: Define $(f+g)(x)$

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

Y. Step2: Substitute given functions

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

Y. Step3: Simplify the expression

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

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W. Step1: Define $(fg)(x)$

$(fg)(x) = f(x) \cdot g(x)$

W. Step2: Substitute given functions

$(fg)(x) = (-x - 4)(x^3 - 3x)$

W. Step3: Expand the product

$(fg)(x) = -x(x^3 - 3x) - 4(x^3 - 3x) = -x^4 + 3x^2 - 4x^3 + 12x$

W. Step4: Rearrange terms

$(fg)(x) = -x^4 - 4x^3 + 3x^2 + 12x$

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M. Step1: Define $(f-g)(x)$

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

M. Step2: Substitute given functions

$(f-g)(x) = (-4x - 5) - (x^3 - x - 4)$

M. Step3: Simplify the expression

$(f-g)(x) = -4x - 5 - x^3 + x + 4 = -x^3 - 3x - 1$

Answer:

E. $(f-g)(x) = 2x^2 + 8x - 5$
Y. $(f+g)(x) = 3x^3 - 2x - 2$
W. $(fg)(x) = -x^4 - 4x^3 + 3x^2 + 12x$
M. $(f-g)(x) = -x^3 - 3x - 1$