the f(x)

Algebra Level 2

If f ( 2 x + 1 ) = 3 x + 2 f(2x+1) = 3x +2 , find f ( 4 x + 3 ) − 6 x f(4x+3) - 6x .


The answer is 5.

Aly Ahmed by Aly Ahmed , 34, Egypt

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2 solutions

Given that

f ( 2 x + 1 ) = 3 x + 2 = 3 2 ( 2 x + 1 ) + 1 2 ⟹ f ( x ) = 3 2 x + 1 2 ∴ f ( 4 x + 3 ) − 6 x = 3 2 ( 4 x + 3 ) + 1 2 − 6 x = 6 x + 9 2 + 1 2 − 6 x = 5 \begin{aligned} f(2x+1) & = 3x + 2 = \frac 32 (2x+1) + \frac 12 \\ \implies f(x) & = \frac 32 x + \frac 12 \\ \therefore f(4x+3) - 6x & = \frac 32(4x+3) + \frac 12 - 6x \\ & = 6x + \frac 92 + \frac 12 - 6x \\ & = \boxed 5 \end{aligned}

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@Chew-Seong Cheong Hello sir .
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Talulah Riley - 3 days, 12 hours ago

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Chew-Seong Cheong - 3 days, 12 hours ago
Saya Suka
Jun 9, 2021

4x + 3 = 2(2x + 1) + 1

Answer
= f(4x + 3) – 6x
= f(2(2x + 1) + 1) – 6x
= [ 3(2x + 1) + 2 ] – 6x
= 6x + 3 + 2 – 6x
= 5

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