Advertisements
Advertisements
प्रश्न
Verify that f and g are inverse functions of each other, where f(x) = x3 + 4, g(x) = `root(3)(x - 4)`
उत्तर
f(x) = x3 + 4
Replacing x by g(x), we get
f[g(x)] = [g(x)]3 + 4
= `(root(3)(x - 4))^3 + 4`
= x – 4 + 4
= x
g(x) = `root(3)(x - 4)`
Replacing x by f(x), we get
g[f(x)] = `root(3)("f"(x) - 4)`
= `root(3)(x^3 + 4 - 4)`
= `root(3)(x^3)`
= x
Since, f[g(x)] = x and g[f(x)] = x.
∴ f and g are inverse functions of each other.
APPEARS IN
संबंधित प्रश्न
Let f : {2, 4, 5} → {2, 3, 6} and g : {2, 3, 6} → {2, 4} be given by f = {(2, 3), (4, 6), (5, 2)} and g = {(2, 4), (3, 4), (6, 2)}. Write down g ° f
If f(x) = 2x2 + 3, g (x) = 5x − 2, then find f ° g
If f(x) = 2x2 + 3, g (x) = 5x − 2, then find g ° g
Verify that f and g are inverse functions of each other, where f(x) = `(x - 7)/4`, g(x) = 4x + 7
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = 8
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(3)
If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(2)
If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(0)
If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(– 3)
If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(5)
If f(x) = 2|x| + 3x, then find f(– 5)
If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(2π), where π = 3.14
If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1)
If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find `"f"(1/4)`
If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 6)
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
|x + 4| ≥ 5
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
|x − 4| + |x − 2| = 3
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
x2 + 7 |x| + 12 = 0
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
|x| ≤ 3
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
2|x| = 5
Answer the following:
Find whether the following function is onto or not.
f : Z → Z defined by f(x) = 6x – 7 for all x ∈ Z
Answer the following:
Find composite of f and g:
f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}
Answer the following:
Find f ° g and g ° f: f(x) = 3x – 2, g(x) = x2
Answer the following:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
1 < |x − 1| < 4
Answer the following:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
`[x/2] + [x/3] = (5x)/6`
Answer the following:
Find f(x) if g(x) = `1 + sqrt(x)` and f[g(x)] = `3 + 2sqrt(x) + x`
Answer the following:
Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`
The inverse of the function y = `(16^x - 16^-x)/(16^x + 16^-x)` is
If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______
If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.
Inverse of the function y = 5 – 10x is ______.
Let f(x) = 1 + x, g(x) = x2 + x + 1, then (f + g) (x) at x = 0 is ______.
If g(x) is the inverse function of f(x) and f'(x) = `1/(1 + x^4)`, then g'(x) is ______.
lf f : [1, ∞) `rightarrow` [2, ∞) is given by f(x) = `x + 1/x`, then f–1(x) is equal to ______.
The value of `int_-1^3 (|x - 2| + [x]) dx` is equal to ______.
(where [.] denotes greatest integer function)
