मराठी

Find Gof And Fog, If F(X) = |X| and G(X) = |5x - 2| - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

`f(x) = |x| and g(x) = |5x - 2|`

:. (gof) (x) = g g(f(x)) = g(|x|) = |5|x|-2|

`(fog)(x) = f(g(x)) = f(|5x - 2|) = ||5x - 2| = |5x - 2`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations and Functions - Exercise 1.3 [पृष्ठ १८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 1 Relations and Functions
Exercise 1.3 | Q 3.1 | पृष्ठ १८

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.


Let f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} be given by = {(1, 2), (3, 5), (4, 1)} and = {(1, 3), (2, 3), (5, 1)}. Write down gof.


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


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


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


If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)).


If f : R → R, f(x) = x and g: R → R , g(x) =  2x+ 1, and R is the set of real numbers, then find fog(x) and gof (x)


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 ______.


Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______ and f o g = ______.


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


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 : R → R, g : R → R and h : R → R are such that f(x) = x2, g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 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 ____________.


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.


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


If f is an invertible function defined as f(x) `= (3"x" - 4)/5,` then f-1(x) is ____________.


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • Two neighbors X and Y ∈ I. X exercised his voting right while Y did not cast her vote in a general election - 2019. Which of the following is true?

`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


Let 'D' be the domain of the real value function on Ir defined by f(x) = `sqrt(25 - x^2)` the D 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


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).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×