CA Foundation Exam > CA Foundation Questions > If f(x) = 2x2 – 5x + 4 then 2f(x) = f(2...
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If f(x) = 2x2 – 5x + 4 then 2f(x) = f(2x) for
- a)x=1
- b)x = – 1
- c)x = ± 1
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If f(x) = 2x2 – 5x + 4 then 2f(x) = f(2x) fora)x=1b)x = – ...
f(x) = 2x^2–5x+4
2(f(x) = 2(2x^2–5x+4 )= 4x^2–10x+8
f(2x) = 2(2x)^2–5(2x)+4 = 8x^2–10x+4
4x^2–10x+8 = 8x^2–10x+4
8x^2–10x+4 -4x^2+10x-8=0
4x^2–4 = 0
take 4 common so 4(x^2–1=0)
4 = 0 , (x^2–1)=0
4 = 0 is negilisable
(x^2–1 = 0)
x ^2 = 1
Answer (x = +1 , -1 )
Most Upvoted Answer
If f(x) = 2x2 – 5x + 4 then 2f(x) = f(2x) fora)x=1b)x = – ...
To determine if 2f(x) is equal to f(2x) for a given value of x, we need to substitute the value of x into both expressions and compare the results.
Given function: f(x) = 2x^2 - 5x + 4
Substituting x = 1:
2f(x) = 2(2x^2 - 5x + 4) = 4x^2 - 10x + 8 = 4(1)^2 - 10(1) + 8 = 4 - 10 + 8 = 2
f(2x) = 2(2x)^2 - 5(2x) + 4 = 2(4x^2) - 10x + 4 = 8x^2 - 10x + 4 = 8(1)^2 - 10(1) + 4 = 8 - 10 + 4 = 2
Hence, for x = 1, we can see that 2f(x) = f(2x) = 2.
Therefore, option C is the correct answer.
Explanation:
1. Substituting x = 1 into the given function f(x) = 2x^2 - 5x + 4.
2. Calculate 2f(x) by multiplying the function by 2.
3. Calculate f(2x) by substituting 2x into the function.
4. Compare the results of 2f(x) and f(2x) for x = 1.
5. Since both expressions evaluate to 2, option C is the correct answer.
6. This process demonstrates that the given equation holds true for x = 1, confirming option C as the correct answer.
Given function: f(x) = 2x^2 - 5x + 4
Substituting x = 1:
2f(x) = 2(2x^2 - 5x + 4) = 4x^2 - 10x + 8 = 4(1)^2 - 10(1) + 8 = 4 - 10 + 8 = 2
f(2x) = 2(2x)^2 - 5(2x) + 4 = 2(4x^2) - 10x + 4 = 8x^2 - 10x + 4 = 8(1)^2 - 10(1) + 4 = 8 - 10 + 4 = 2
Hence, for x = 1, we can see that 2f(x) = f(2x) = 2.
Therefore, option C is the correct answer.
Explanation:
1. Substituting x = 1 into the given function f(x) = 2x^2 - 5x + 4.
2. Calculate 2f(x) by multiplying the function by 2.
3. Calculate f(2x) by substituting 2x into the function.
4. Compare the results of 2f(x) and f(2x) for x = 1.
5. Since both expressions evaluate to 2, option C is the correct answer.
6. This process demonstrates that the given equation holds true for x = 1, confirming option C as the correct answer.
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If f(x) = 2x2 – 5x + 4 then 2f(x) = f(2x) fora)x=1b)x = – 1c)x = ± 1d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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