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It is given that
f(a,b) = logb α
g(x) = x3 - 2x2 + 7x + 11
h(x) = 2x + 1
Find the sum of values of x for which the following equality holds
f(g(x),h(x)) = 2
Correct answer is '7'. Can you explain this answer?
Most Upvoted Answer
It is given thatf(a,b) =logbαg(x) =x3 - 2x2 + 7x + 11h(x) = 2x +...
f(g(x),h(x)) = 2
logh(x) g (x) = 2
log2x+1 x3 − 2x2 + 7x + 11 = 2
(2x+1)2 = x3 − 2x2 + 7x + 11
4x2 + 4x + 1 = x3 − 2x2 + 7x + 11
x3 − 6x2 + 3x + 10 = 0
Also, x = -1 satisfies the above equation. Hence, (x+1) is a factor of the expression.
Using algebraic division and further factorization, we get
(x+1) (x-2) (x-5) = 0
Hence, the roots are -1, 2 and 5.
But if we consider -1, the base of the logarithm, 2x + 1 becomes -1, which is not possible, hence the only possible values are 2 and 5.
Hence, sum = 7.
Community Answer
It is given thatf(a,b) =logbαg(x) =x3 - 2x2 + 7x + 11h(x) = 2x +...
The given function is f(a,b) = logb(a), which represents the logarithm of a with base b.
This function takes two inputs, a and b, and returns the logarithm of a with base b. The logarithm function is a mathematical function that represents the exponent to which the base (b) must be raised to obtain the value (a).
For example, if we have f(9, 3), it means we want to find the logarithm of 9 with base 3. The logarithm of 9 with base 3 is 2, since 3 raised to the power of 2 equals 9 (3^2 = 9).
Similarly, if we have f(16, 2), it means we want to find the logarithm of 16 with base 2. The logarithm of 16 with base 2 is 4, since 2 raised to the power of 4 equals 16 (2^4 = 16).
In general, the logarithm function helps us find the exponent needed to raise the base to obtain a certain value.
This function takes two inputs, a and b, and returns the logarithm of a with base b. The logarithm function is a mathematical function that represents the exponent to which the base (b) must be raised to obtain the value (a).
For example, if we have f(9, 3), it means we want to find the logarithm of 9 with base 3. The logarithm of 9 with base 3 is 2, since 3 raised to the power of 2 equals 9 (3^2 = 9).
Similarly, if we have f(16, 2), it means we want to find the logarithm of 16 with base 2. The logarithm of 16 with base 2 is 4, since 2 raised to the power of 4 equals 16 (2^4 = 16).
In general, the logarithm function helps us find the exponent needed to raise the base to obtain a certain value.
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It is given thatf(a,b) =logbαg(x) =x3 - 2x2 + 7x + 11h(x) = 2x +1Find the sum of values of x for which the following equality holdsf(g(x),h(x)) = 2Correct answer is '7'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about It is given thatf(a,b) =logbαg(x) =x3 - 2x2 + 7x + 11h(x) = 2x +1Find the sum of values of x for which the following equality holdsf(g(x),h(x)) = 2Correct answer is '7'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is given thatf(a,b) =logbαg(x) =x3 - 2x2 + 7x + 11h(x) = 2x +1Find the sum of values of x for which the following equality holdsf(g(x),h(x)) = 2Correct answer is '7'. Can you explain this answer?.
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