Advertisements
Advertisements
Question
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
Solution 1
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.
Solution 2
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
RELATED QUESTIONS
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 f ° f
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = 9x3 + 8
If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(0.5)
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(– 1.2)
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.
2|x| = 5
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
[x + [x + [x]]] = 9
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} = 0
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
{x} = 0.5
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 whether the following function is onto or not.
f : R → R defined by f(x) = x2 + 3 for all x ∈ R
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) = 256x4, g(x) = `sqrt(x)`
Answer the following:
If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (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
−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
[x − 2] + [x + 2] + {x} = 0
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = ex, g(x) = log x
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) = `x/sqrt(1 + x^2)`
Answer the following:
Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`
If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______
If f(x) =bx - 7 and f(-1) = 4, then b = ______.
If f(x) =x4, g(x) = 6x – 2, then g[f(x)] = ______.
Let f(x) = 1 + x, g(x) = x2 + x + 1, then (f + g) (x) at x = 0 is ______.
lf f : [1, ∞) `rightarrow` [2, ∞) is given by f(x) = `x + 1/x`, then f–1(x) is equal to ______.
If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is ______.
(where [.] denotes the greatest integer function)
