Advertisements
Advertisements
प्रश्न
If f(x) = [4 – (x – 7)3]1/5 is a real invertible function, then find f–1(x).
उत्तर
Given f(x) = [4 – (x – 7)3]1/5 is a real invertible function.
Let f(x) = y
`\implies` y = [4 – (x – 7)3]1/5
`\implies` y5 = 4 – (x – 7)3
`\implies` (x – 7)3 = 4 – y5
`\implies` x – 7 = [4 – y5]1/3
`\implies` x = 7 + (4 – y5)1/3
`\implies` f1(y) = 7 + (4 – y5)1/3 ` {{:(∵ f(x) "is invertible"), (∴ f(x) = "y"),(\implies x = f^-1("y")):}`
Hence f1(x) = 7 + (4 – x5)1/3
APPEARS IN
संबंधित प्रश्न
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?
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 f: R → R given by f(x) = 4x + 3. Show that f is invertible. Find 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.
If f: R → R 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: 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.
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 ______.
The composition of functions is commutative.
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(x) = `(3"x" + 2)/(5"x" - 3)` then (fof)(x) is ____________.
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.
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.
If `f(x) = 1/(x - 1)`, `g(x) = 1/((x + 1)(x - 1))`, then the number of integers which are not in domian of gof(x) are
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: 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
Let `f : R {(-1)/3} → R - {0}` be defined as `f(x) = 5/(3x + 1)` is invertible. Find f–1(x).
