Advertisements
Advertisements
Question
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).
Advertisements
Solution
Given:
f(x) = 2x − 3
g(x) = x3 + 5
(fog)(x)=f[g(x)]
=f(x3+5)
=2(x3+5)−3
=2x3+10−3
=2x3+7
Let (fog)(x)=y
⇒2x3+7=y
`=>x=((y-7)/2)^(1/3)`
`=>(fog)^-1 (y)=((y-7)/2)^(1/3)`
Thus, (fog)−1: R→R be defined by `(fog)^-1 (x)=((x-7)/2)^(1/3)`
APPEARS IN
RELATED QUESTIONS
Find gof and fog, if f(x) = |x| and g(x) = |5x – 2|.
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)}
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 f: R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.
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).
If f: R → R be given by `f(x) = (3 - x^3)^(1/3)`, then fof(x) is ______.
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}` given by
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 ______.
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 ____________.
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.
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?
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
