मराठी

Let f: N → R be the function defined by f(x) = 2x-12 and g: Q → R be another function defined by g(x) = x + 2. Then (g o f) 32 is ______.

Advertisements
Advertisements

प्रश्न

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 ______.

पर्याय

  • 1

  • 1

  • `7/2`

  • None of these

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

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 none of these.

Explanation:

We have f(x) = `(2x - 1)/2` and g(x) = x + 2

gof`(3/2)` = g`(f(3/2))`

= `"g"((2 xx 3/2 - 1)/2)`

= g(1) = 1 + 2

= 3

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Exercise [पृष्ठ १६]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 1 Relations And Functions
Exercise | Q 45 | पृष्ठ १६

व्हिडिओ 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).


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.


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?


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


Let f: X → 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 ∈ Y, fog1(y) = IY(y) = fog2(y). Use one-one ness of f).


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


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


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


The composition of functions is associative.


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


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 ____________.


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


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


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


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


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


Which statement correctly describes an onto (surjective) function?


What is the necessary and sufficient condition for a function to be invertible?


Which property of inverse functions is represented by \((f^{-1})^{-1}=f\)?


According to the Reflective Property, the graph of \(f^{-1}\) is the exact reflection of the graph of \(f\) across which line?


For \(f(x)=4x+3\), where \(Y=\{y\in\mathbb{N}:y=4x+3\text{ for some }x\in\mathbb{N}\}\), what is the inverse function \(g:Y\to\mathbb{N}\)?


For \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=10x+7\), which function satisfies \(g\circ f=f\circ g=I_R\)?


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?


Which statement expresses that an inverse is unique whenever it exists?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×