हिंदी

Every function is invertible. - Mathematics

Advertisements
Advertisements

प्रश्न

Every function is invertible.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

Explanation:

Only bijective functions are invertible.

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

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 61 | पृष्ठ १७

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).


Let f : W → W be defined as

`f(n)={(n-1, " if n is odd"),(n+1, "if n is even") :}`

Show that f is invertible a nd find the inverse of f. Here, W is the set of all whole
numbers.


Find goand fog, if `f(x) = 8x^3` and `g(x) = x^(1/3)`

 


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)}


Consider fR → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.


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


Consider f: `R_+ -> [-5, oo]` given by `f(x) = 9x^2 + 6x - 5`. Show that f is invertible with `f^(-1) (y) ((sqrt(y + 6)-1)/3)`

Hence Find

1) `f^(-1)(10)`

2) y if `f^(-1) (y) = 4/3`

where R+ is the set of all non-negative real numbers.


Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? If g is described by g (x) = αx + β, then what value should be assigned to α and β


Let f: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is ______.


Let f: N → R be the function defined by f(x) = `(2x - 1)/2` and g: Q → R be another function defined by g(x) = x + 2. Then (g o f) `3/2` is ______.


The composition of functions is associative.


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 ____________.


Let f : N → R : f(x) = `((2"x"−1))/2` and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) `(3/2)` is ____________.


Let f : R – `{3/5}`→ R be defined by f(x) = `(3"x" + 2)/(5"x" - 3)` Then ____________.


Which one of the following functions is not invertible?


If f : R → R defind by f(x) = `(2"x" - 7)/4` is an invertible function, then find f-1.


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


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


If `f(x) = 1/(x - 1)`, `g(x) = 1/((x + 1)(x - 1))`, then the number of integers which are not in domian of gof(x) are


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: A → B and G B → C are one – one, then g of A → C is


If f: N → Y be a function defined as f(x) = 4x + 3, Where Y = {y ∈ N: y = 4x+ 3 for some x ∈ N} then function is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×