Question No 54.Let f(x) and h(x) be functions defined as f(x) = 2x + 4 and h(x) = 2(2x – 2) – 2(x + 2) + 16. Find the largest value of 'x' such that f(x) = 4h(x).
Question
Question No 54.Let f(x) and h(x) be functions defined as f(x) = 2x + 4 and h(x) = 2(2x – 2) – 2(x + 2) + 16. Find the largest value of 'x' such that f(x) = 4h(x).
Solution
To solve this problem, we first need to simplify the equation f(x) = 4h(x).
Given that f(x) = 2x + 4 and h(x) = 2(2x – 2) – 2(x + 2) + 16, we can substitute these into the equation:
2x + 4 = 4[2(2x – 2) – 2(x + 2) + 16]
Simplify the right side of the equation:
2x + 4 = 4[4x - 4 - 2x - 4 + 16]
2x + 4 = 4[2x + 8]
2x + 4 = 8x + 32
Now, we can solve for x:
2x - 8x = 32 - 4
-6x = 28
x = 28 / -6
x = -14/3
Therefore, the largest value of 'x' such that f(x) = 4h(x) is -14/3.
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