Advertisements
Advertisements
प्रश्न
Find gof and fog, if f(x) = 8x3 and `g(x) = x^(1/3)`.
Advertisements
उत्तर
f(x) = 8x3 and `g(x) = x^(1/3)`
∴ (gof)(x) = g(f(x))
= g(8x3)
= `(8x^3)^(1/3)`
= 2x
(fog)(x) = f(g(x))
= `f(x^(1/3))`
= `8(x^(1/3))^3`
= 8x
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: {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)
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+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f−1 of given f by `f^(-1)(y) = sqrt(y - 4)`, where R+ is the set of all non-negative real numbers.
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 the inverse of f−1 is f, i.e., (f−1)−1 = f.
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.
If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)).
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.
If f : R → R, f(x) = x3 and g: R → R , g(x) = 2x2 + 1, and R is the set of real numbers, then find fog(x) and gof (x)
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 ______.
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(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 ____________.
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.
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?
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:-
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
What is the function \(g\) called when \(g\circ f=I_X\) and \(f\circ g=I_Y\)?
Which statement correctly describes a one-one (injective) function?
A function that is both one-one and onto is called what?
Which property of inverse functions is represented by \((f^{-1})^{-1}=f\)?
Which equation expresses that applying a function and then its inverse returns the original input?
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 \(g\circ f=f\circ g=I_R\)?
What are the domain and range of the inverse function in the graphical example?
