Question:
The functions f(x) and g(x) are related as f(g(x)) = xg(f(f(x))), where f (x) = \(\frac{x}{x-1}\). What could be the functional form g(x)?
The functions f(x) and g(x) are related as f(g(x)) = xg(f(f(x))), where f (x) = \(\frac{x}{x-1}\). What could be the functional form g(x)?
Updated On: Jan 12, 2025
- \(\frac{1}{x}\)
- \(\frac{x}{x+1}\)
- \(\frac{x+1}{x}\)
- \(\frac{x}{x-1}\)
- \(\frac{x}{1-x}\)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct option is (C): \(\frac{x+1}{x}\)
Was this answer helpful?
0
1
Top Questions on Functions
- Suppose \(f(x,y)\) is a real-valued function such that \(f(3x+2y,2x-5y)=19x\), for all real numbers \(x\) and \(y\) . The value of x for which \(f(x,2x) = 27\) , is
- Let r be a real number and \(f(x) = \begin{cases} 2x - r & \text{if } x \geq r \\ r & \text{if } x < r \end{cases}\).Then, the equation \(f(x)=f(f(x))\) holds for all real values of x where
- Suppose for all integers x, there are two functions f and g such that \(f(x)+f(x−1)−1=0\) and \(g(x)=x^2\). If \(f(x^2−x)=5\),then the value of the sum \(f(g(5))+g(f(5))\) is
- Let \(f(x)=x^2+ax+b\) and \(g(x)=f(x+1)-f(x-1)\). If \(f(x)≥0\) for all real \(x\), and \(g(20)=72\), then the smallest possible value of \(b\) is
Questions Asked in IBSAT exam
- Lumber : Bear :: Waddle :
Directions: In the question, the first two words are related in a particular manner. You have to choose a word from the options so that a new pair of words is formed where the relation is the same as that of the first pair of words. You are required to consider the secondary meaning of certain words while choosing an answer.- IBSAT
- Analogy
- A boy has some coins with some value on them. He arranges the coins in the form of a star as shown below such that the sums of the numbers in the four circles along any line segment of the star are all equal. What is the sum of the missing numbers?
- IBSAT
- Logical and Analytical Reasoning Skills
- Directions: Fill in the blanks with the words that best fit the meaning of the sentence as a whole.
If a nation is unable to come to ______ on interpreting its own past, it will be unable to ______ its national interests.- IBSAT
- Fill in the Blanks
- If p, q, r and s are four positive integers such that pqrs = 1, what is the minimum value of (2 + p)(3 + q)(4 + r)(5 + s)?
- IBSAT
- Quadratic Equation
- There are two solid pyramids, each having 8 edges of length 8 cm each. These two pyramids are moulded to form a hexagonal pyramid with length of each side as 8 cm. What is the slant height of the new pyramid?
- IBSAT
- Geometry
View More Questions