Exams › GATE › Engineering Mathematics

f(x) and g(y) are functions of x and y, respectively, and f(x) = g(y) for all real values of x and y. Which one of the following options is necessarily TRUE for all x and y?

1. f(x) = 0 and g(y) = 0
2. f(x) = g(y) = constant
3. f(x) ≠ constant and g(y) ≠ constant
4. f(x) + g(y) = f(x) − g(y)

Correct answer: f(x) = g(y) = constant

Solution

The correct option is true because if f(x) equals g(y) for all real values of x and y, then both functions must take on the same constant value across their entire domains to maintain equality.

Related GATE Engineering Mathematics questions

• The sum of the following infinite series is: 1/1! + 1/2! + 1/3! + 1/4! + 1/5! +...
• Which one of the following options is the correct Fourier series of the periodic function f(x) described below: f(x) = { 0 if −2 < x < −1 { 2k if −1 < x < 1; period = 4 { 0 if 1 < x < 2
• The value of lim_(x→∞) (x − √(x² + x)) is equal to
• The following inequality is true for all x close to 0. 2 − x²/3 < x sin x/(1 − cos x) < 2 What is the value of lim(x→0) x sin x/(1 − cos x) ?
• A closed thin-walled tube has thickness, t, mean enclosed area within the boundary of the centreline of tube’s thickness, Aₘ, and shear stress, τ. Torsional moment of resistance, T, of the section would be
• Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m³) when the depth of water at the centre of the tank is 6 m?

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →