Question

Find R(x)=f(x)+g(x) where f(x)= 9/5x2−9x+4 and g(x)= 10x/5x2−14x+8

Which of the following represents the function
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(
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)
f(x)?
a)
9
5
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2
−
9
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+
4
5
9
​
x
2
−9x+4
b)
10
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5
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2
−
14
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+
8
5x
2
−14x+8
10x
​

c)
9
5
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2
−
9
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−
4
5
9
​
x
2
−9x−4
d)
10
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5
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2
+
14
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+
8
5x
2
+14x+8
10x
​

Answer 1

The correct representation of the function R(x) = f(x) + g(x) is (option a) (9/5)x² - 9x + 4.

Step-by-step explanation:

To find R(x) = f(x) + g(x), add the expressions for f(x) and g(x):

R(x) = (9/5)x² - 9x + 4 + 10x / (5x² - 14x + 8)

The common denominator for addition is 5x² - 14x + 8. Combine the terms:

R(x) = (9/5)x² - 9x + 4 + (10x² - 14x) / (5x² - 14x + 8)

Combine the numerators:

R(x) = (9/5)x² - 9x + 4 + 2x(5x - 7) / (5x - 4)(x - 2)

Now, the expression for R(x) is simplified. Comparing this with the given options, the correct representation is option a) (9/5)x² - 9x + 4.

Understanding how to combine and simplify algebraic expressions is essential for accurately representing composite functions (option a). In this case, finding the common denominator and combining terms allows us to determine the correct representation for R(x) = f(x) + g(x).