हिंदी

The composition of functions is commutative.

Advertisements
Advertisements

प्रश्न

The composition of functions is commutative.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

Let f(x) = x2 and g(x) = x + 1

fog(x) = f((g(x))

= f(x + 1)

= (x + 1)2

= x2 + 2x + 1

gof(x) = g(f(x))

= g(x2)

= x2 + 1

Thus fog(x) ≠ gof(x)

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Exercise [पृष्ठ १७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 59 | पृष्ठ १७

वीडियो ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्न

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x).


Find gof and fog, if f(x) = |x| and g(x) = |5x – 2|.


If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3` show that fof(x) = x, for all `x ≠ 2/3`. What is the inverse of f?


State with reason whether following functions have inverse

f: {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}


State with reason whether following functions have inverse 

h: {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}


Show that f: [–1, 1] → R, given by f(x) = `x/(x + 2)`  is one-one. Find the inverse of the function f: [–1, 1] → Range f.

(Hint: For y in Range f, y = `f(x) = x/(x + 2)` for some x in [–1, 1] i.e., `x = (2y)/(1 - y)`)


Consider f: R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f−1 of given f by `f^(-1)(y) = sqrt(y - 4)`, where R+ is the set of all non-negative real numbers.


Consider f: {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f−1 and show that (f−1)−1 = f.


Let f: R → R be the function defined by f(x) = sin (3x+2) ∀ x ∈ R. Then f is invertible.


If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = `sqrtpi/2` will be ____________.


If f(x) = `(3"x" + 2)/(5"x" - 3)` then (fof)(x) is ____________.


Let f : R → R be the functions defined by f(x) = x3 + 5. Then f-1(x) is ____________.


If f(x) = (ax2 – b)3, then the function g such that f{g(x)} = g{f(x)} is given by ____________.


Which one of the following functions is not invertible?


Consider the function f in `"A = R" - {2/3}` defiend as `"f"("x") = (4"x" + 3)/(6"x" - 4)` Find f-1.


If f : R → R defined by f(x) `= (3"x" + 5)/2` is an invertible function, then find f-1.


`f : x -> sqrt((3x^2 - 1)` and `g : x -> sin (x)` then `gof : x ->`?


The domain of definition of f(x) = log x2 – x + 1) (2x2 – 7x + 9) is:-


Domain of the function defined by `f(x) = 1/sqrt(sin^2 - x) log_10 (cos^-1 x)` is:-


Let A = `{3/5}` and B = `{7/5}` Let f: A → B: f(x) = `(7x + 4)/(5x - 3)` and g:B → A: g(y) = `(3y + 4)/(5y - 7)` then (gof) is equal to


If f(x) = [4 – (x – 7)3]1/5 is a real invertible function, then find f–1(x).


Let `f : R {(-1)/3} → R - {0}` be defined as `f(x) = 5/(3x + 1)` is invertible. Find f–1(x).


What is the function \(g\) called when \(g\circ f=I_X\) and \(f\circ g=I_Y\)?


Which statement correctly describes a one-one (injective) function?


Which statement correctly describes an onto (surjective) function?


Which equation expresses that applying a function and then its inverse returns the original input?


Which sequence gives the standard method to find an inverse of a function?


For \(f:\mathbb{R}\to(-1,1)\) defined by \(f(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}\), what is \(f^{-1}(x)\)?


In the graphical example, what are the domain and range of the given function?


What are the domain and range of the inverse function in the graphical example?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×