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3 years ago

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

1 answer:

6 0

A:

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

(f+g)(x)=4x-5+3x+9

(f+g)(x)=7x+4

B:

(f•g)(x)=f(x)•g(x)

(f•g)(x)=(4x-5)(3x+9)

(f•g)(x)=12x^2-15x+36x-45

(f•g)(x)=12x^2+21x-45

C:

(f○g)(x)=f(g(x))

(f○g)(x)=4(3x+9)-5

(f○g)(x)=12x+36-5

(f○g)(x)=12x+31

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Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?

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Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3$

To find the value of the given expression:

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}$

( By using the property ( $(\frac{a}{b})^m=\frac{a^m}{b^m}$ )

$=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}$

( By using the property $(ab)^m=a^mb^m$ )

$=\frac{(10^{12})(5^6)}{(10^9)(5^9)}$

( By using the property $(a^m)^n=a^{mn}$ )

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( By using the property $\frac{1}{a^m}=a^{-m}$ )

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$=\frac{10^3}{5^3}$ ( By using the property $a^{-m}=\frac{1}{a^m}$ )

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Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Therefore the value to the given expression is 8

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