HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Answer the following:

If A = {−1, 1} , find A × A × A

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 f ° 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

Verify that f and g are inverse functions of each other, where f(x) = x³ + 4, g(x) = `root(3)(x - 4)`

Verify that f and g are inverse functions of each other, where f(x) = `(x + 3)/(x - 2)`, g(x) = `(2x + 3)/(x - 1)`

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`

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

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(– 4)

If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(– 3)