Composition Of Functions

Question

Let f(x) = 2x + 3 and g(x) = x^2 - 1 be real functions; the value of the composite (f ∘ g)(2) minus (g ∘ f)(0) equals which number?

RankGuru · Accepted Answer

Function composition applies one function to the output of another, with (f ∘ g)(x) meaning f(g(x)), a foundational operation in JEE Advanced function problems. Compute (f ∘ g)(2): first g(2) = 2^2 - 1 = 3, then f(3) = 2·3 + 3 = 9. Compute (g ∘ f)(0): first f(0) = 2·0 + 3 = 3, then g(3) = 3^2 - 1 = 8. The required difference is 9 - 8 = 1. Order matters because composition is generally non-commutative, which this problem deliberately tests. Option 9 reports only the first composite, ignoring the subtraction. Option -1 reverses the order of subtraction. Option 5 results from mistakenly computing g(f(0)) as 2·3 - 1. Hence the answer is 1. Plausibility check: since f ∘ g and g ∘ f differ here (9 versus 8), their near-equality confirms the expected non-commutativity of composition without the functions being inverses, consistent with the standard composition pattern.

Composition Of Functions

Select the correct option:

🔒 Solution Hidden from View

More sets, relations and functions Practice Questions

The number of real solutions of the equation given by the absolute value |x - 1| + |x - 3| = 4 over ...

If set A has 3 elements and set B has 4 elements, then the number of subsets of the Cartesian produc...

A function f from positive reals to reals satisfies f(xy) = f(x) + f(y) for all positive x, y, and f...

Let f from real numbers to real numbers be defined by f(x) = x^3 + x + 1; which statement about the ...

The total number of functions that can be defined from a set with 5 elements to a set with 3 element...

For finite sets the symmetric difference A Δ B is defined as the set of elements in exactly one of A...

For the signum function sgn(x), which equals -1, 0, or 1 according to the sign of x, the value of th...

For the real function g(x) = (x^2 + x + 1)/(x^2 + x + 2) defined for every real x, the complete rang...

The real function defined by the rule f(x) = the square root of (x - 3) added to the square root of ...

Which of the following real functions defined for all real x is an odd function according to the sym...

If the function f from real numbers to real numbers is defined by f(x) = (3x - 2)/(x + 4) for x not ...

Let [x] denote the greatest integer not exceeding x; the value of the sum [2.7] + [-2.7] + [0.4] + [...

About This Question

Solution