Advertisements
Advertisements
Question
Answer the following:
If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (x) = x
Advertisements
Solution
(f ° f) (x) = f[f(x)]
= `"f"[(2x - 1)/(5x - 2)]`
= `(2((2x - 1)/(5x - 2)) - 1)/(5((2x - 1)/(5x - 2)) - 2)`
= `(2(2x - 1) - (5x - 2))/(5(2x - 1) - 2(5x - 2)`
= `(4x - 2 - 5x + 2)/(10x - 5 - 10x + 4)`
= `(-x)/(-1)`
= x
APPEARS IN
RELATED QUESTIONS
If f(x) = 2x2 + 3, g(x) = 5x − 2, then find g ° f
Check if the following function has an inverse function. If yes, find the inverse function.
f(x) = `sqrt(4x + 5)`
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(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(– 4)
If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(1)
If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(7.2)
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(– 6)
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} > 4
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.
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 composite of f and g:
f = {(1, 3), (2, 4), (3, 5), (4, 6)}
g = {(3, 6), (4, 8), (5, 10), (6, 12)}
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) = x2 + 5, g(x) = x – 8
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
[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 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 ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`
Let F(x) = ex, G(x) = e-x and H(x) = G[F(x)], where x is a real variable. Then `"dH"/"dx"`at x = 0 is ______.
If f(x) = `sin^2x + sin^2(x + pi/3) + cosx cos(x + pi/3) and g(5/4) = 1`, then (gof)(x) is equal to: ______
If f(x) =bx - 7 and f(-1) = 4, then b = ______.
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 ______.
Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.
