Advertisements
Advertisements
प्रश्न
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):}`
Advertisements
उत्तर १
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
If x < 0, x + 7 < 7
If x ≥ 0, – x ≤ 0 so that 8 – x ≤ 8
∴ Range = `(- ∞, 8)`
∴ for y = 10, we cannot find x such that f(x) = y
∴ f is not onto
∴ f–1 does not exist.
उत्तर २
f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`
∴ f(– 1) = – 1 + 7 = 6
∴ f(2) = 8 – 2 = 6
∴ f(– 1) = f(2) but – 1 ≠ 2
∴ f is not one-one
∴ f–1 does not exist.
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 ° f
If f(x) = 2x2 + 3, g (x) = 5x − 2, then find g ° g
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = 5x2
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) = `(6x - 7)/3`
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(1)
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(2)
If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(0.5)
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)`
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} > 4
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} = 0.5
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
2{x} = x + [x]
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 f ° g and g ° f : f(x) = x2 + 5, g(x) = x – 8
Answer the following:
If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (x) = x
Answer the following:
If f(x) = `(x + 3)/(4x - 5)`, g(x) = `(3 + 5x)/(4x - 1)` then show that (f ° g) (x) = x
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
−2 < [x] ≤ 7
Answer the following:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
2[2x − 5] − 1 = 7
Answer the following:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
[x2] − 5[x] + 6 = 0
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 + 2] + {x} = 0
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = ex, g(x) = log x
For f(x) = [x] , where [x] is the greatest integer function, which of the following is true, for every x ∈ R.
`int_0^4 x[x] dx`, where [.] denotes the greatest integer function, equals ______
If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.
If g(x) is the inverse function of f(x) and f'(x) = `1/(1 + x^4)`, then g'(x) is ______.
`int_0^3 [x]dx` = ______, where [x] is greatest integer function.
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)
