हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

f(x) = |x| and g(x) = |5x – 2|

∴ (gof)(x) = g(f(x)) 

= g(|x|)

= |5|x| – 2|

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

= f(|5x – 2|)

= ||5x – 2|| 

= |5x – 2|

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations and Functions - EXERCISE 1.3 [पृष्ठ १८]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 1 Relations and Functions
EXERCISE 1.3 | Q 3. (i) | पृष्ठ १८

वीडियो ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्न

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


Let f, g and h be functions from R to R. Show that

(f + g)oh = foh + goh

(f · g)oh = (foh)·(goh)


Find gof and fog, if f(x) = 8x3 and `g(x) = x^(1/3)`.


State with reason whether following functions have inverse

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


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] ie x = `2y/(1-y)`


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.


Let fX → Y be an invertible function. Show that f has unique inverse. (Hint: suppose g1 and g2 are two inverses of f. Then for all y ∈ Yfog1(y) = IY(y) = fog2(y). Use one-one ness 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.


Let fX → Y be an invertible function. Show that the inverse of f−1 is f, i.e., (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.


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.


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: [0, 1] → [0, 1] be defined by f(x) = `{{:(x",",  "if"  x  "is rational"),(1 - x",",  "if"  x  "is irrational"):}`. Then (f o f) x 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 = ______.


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


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


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


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


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:-


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


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×