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Q. (Function) A function f(x) = ax + 3 satisfies f(-2) = 5 and 4f(-3) - 3f(2) + f(x) = 9. What is the value of x

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Q. (Function) A function f(x) = ax + 3 satisfies f(-2) = 5 and 4f(-3) - 3f(2) + f(x) = 9. What is the value of x

by Max@Math Revolution » Sun Aug 30, 2020 8:21 am

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Q. (Function) A function f(x) = ax + 3 satisfies f(-2) = 5 and 4f(-3) - 3f(2) + f(x) = 9. What is the value of x?

A. 10
B. 13
C. 15
D. 18
E. 20
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Re: Q. (Function) A function f(x) = ax + 3 satisfies f(-2) = 5 and 4f(-3) - 3f(2) + f(x) = 9. What is the value of x

by Max@Math Revolution » Tue Sep 01, 2020 2:06 am
Solution:

Solution:

If 4f(-3) - 3f(2) + f(x) = 9, we have to find the value of x.

Given: f(x) = ax + 3 satisfies f(-2) = 5.

Substitute x = -2 into f(x) = ax + 3.

=> f(-2) = a(-2) + 3 = 5
=> -2a + 3 = 5
=> -2a = 5 – 3 = 2
=> a = -1

So, we get f(x) = -x + 3.

Therefore, we get f(-3) = -(-3) + 3 = 6 and f(2) = -2 + 3 = 1.

=> Substituting the values of f(-3) and f(2) into 4f(-3) - 3f(2) + f(x) = 9 gives us
4(6) – 3(1) + f(x) = 9 or 24 – 3 + f(x) = 9.

=> Substituting the value of f(x) = -x + 3 into 24 – 3 + f(x) = 9 gives us
24 - 3 - x + 3 = 9 or x = 24 – 9 = 15.

Therefore, C is the correct answer.

Answer: C
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