Exams › JEE Advanced › Maths

Let a and b be real constants and define f(x) = a sin x + b * cbrt(x) + 4 for all real x. Given that f(log10(log3 10)) = 5, evaluate f(log10(log10 3)).

1. 3
2. 5
3. 4
4. cannot be determined

Correct answer: 3

Solution

Let p = log10(log3 10). Since log10 3 = 1/(log3 10), log10(log10 3) = -log10(log3 10) = -p. With g(x) = a sin x + b*cbrt(x) odd, g(-p) = -g(p). Given f(p) = g(p) + 4 = 5 => g(p) = 1. Then f(-p) = -g(p) + 4 = -1 + 4 = 3.

Related JEE Advanced Maths questions

• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• The relation x² = xy can be described as:
• Consider the function f: R → R given by f(x) = (e^x - e^(-x)) / (e^x + e^(-x)). Which of the following statements is accurate?
• Consider the functions f(x) = max {1 + sin(x), 1 - cos(x)} for x in the interval [0, 2π], and g(x) = max {1, |x - 1|} for x belonging to the set of real numbers. Which of the following is true?
• Given f(x + f(y)) = f(x) + y, x, y ∈ R. Find f(1000).
• Find the range of fog(x) = f(g(x)) = f(4x(1 − x)).

⚔️ Practice JEE Advanced Maths free + battle 1v1 →