Advertisements
Advertisements
Question
Verify that f and g are inverse functions of each other, where f(x) = `(x + 3)/(x - 2)`, g(x) = `(2x + 3)/(x - 1)`
Advertisements
Solution
f(x) = `(x + 3)/(x - 2)`, g(x) = `(2x + 3)/(x - 1)`
Replacing x by g(x), we get
f[g(x)] = `("g"(x)+3)/("g"(x)-2)`
= `(((2x + 3)/(x - 1)) + 3)/(((2x + 3)/(x - 1)) - 2)`
= `(2x + 3 + 3x -3)/(2x + 3 - 2x +2)`
= `(5x)/5`
= x
g(x) = `(2x+3)/(x-1)`
Replacing x by f(x), we get
g[f(x)] = `("2f"(x) + 3)/("f"(x) - 1)`
= `(2((x + 3)/(x - 2)) + 3)/(((x + 3)/(x - 2)) - 1)`
= `(2x+6+3x-6)/(x+3-x+2)`
= `(5x)/5`
= x
Since, f [g(x)] = x and g[f(x)] = x.
∴ f and g are inverse functions of each other.
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 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) = 5x2
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) = 9x3 + 8
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(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(7.2)
If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find `"f"(- 5/2)`
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"(1/4)`
If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1.2)
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| ≤ 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} = 0.5
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:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
|x2 − x − 6| = x + 2
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
[x2] − 5[x] + 6 = 0
If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______
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 ______.
Inverse of the function y = 5 – 10x is ______.
The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` 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)
