English

If f(x) = {4x-2,x≤-35,-3<x<3x2,x≥3, then find f(1)

Advertisements
Advertisements

Question

If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(1)

Sum
Advertisements

Solution

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

f(1) = 5

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Functions - Exercise 6.2 [Page 128]

RELATED QUESTIONS

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


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) = 8


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


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"(- 5/2)`


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"(1/4)`


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.

x2 + 7 |x| + 12 = 0


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.

[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


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 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 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

2[2x − 5] − 1 = 7


If `a + pi/2 < 2tan^-1x + 3cot^-1x < b`, then a and b are respectively.


`int_0^4 x[x]  dx`, where [.] denotes the greatest integer function, equals ______


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 ______.


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 ______.


`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 ______.


If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is ______.

(where [.] denotes the greatest integer function)


The value of `int_-1^3 (|x - 2| + [x])  dx` is equal to ______.

(where [.] denotes greatest integer function)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×