मराठी

Find Gof And Fog, If `F(X) = 8x^3` and `G(X) = X^(1/3)` - Mathematics

Advertisements
Advertisements

प्रश्न

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

 

उत्तर

`f(x) = 8x^3 and g(x) = x^(1/3)`

`:. (gof)(x) = g(f(x)) = g(8x^3) = (8x^3)^(1/3)  =2x`

`(fog) (x) = f(g(x)) = f(x^(1/3)) = 8(x^(1/3))^3 = 8x`

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 3.2 | 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).


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


Consider fR+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^(-1)(y) = ((sqrt(y +6) - 1)/3)`


If f→ be given by `f(x) = (3 - x^3)^(1/3)` , then fof(x) is 

(A) `1/(x^3)`

(B) x3

(C) x

(D) (3 − x3)


Let `f:R - {-4/3} -> R` be a function defined as `f(x) = (4x)/(3x + 4)`. The inverse of f is map g Range `f -> R -{- 4/3}`

(A) `g(y) = (3y)/(3-4y)`

(B) `g(y) = (4y)/(4 - 3y)`

(C) `g(y) = (4y)/(3 - 4y)` 

(D) `g(y) = (3y)/(4 - 3y)`


Let f: W → W be defined as f(n) = n − 1, if is odd and f(n) = n + 1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.


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.


Let f : W → W be defined as f(x) = x − 1 if x is odd and f(x) = x + 1 if x is even. Show that f is invertible. Find the inverse of f, where W is the set of all whole numbers.


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)


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: A → B and g: B → C be the bijective functions. Then (g o f)–1 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 = ______.


The composition of functions is associative.


Every function is invertible.


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 ____________.


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 ____________.


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?


The inverse of the function `"y" = (10^"x" - 10^-"x")/(10^"x" + 10^-"x")` is ____________.


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


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: 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


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×