English

If f(x) = {x2+3x≤25x+7x>2, then find f(0)

Advertisements
Advertisements

Question

If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(0)

Sum
Advertisements

Solution

f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`

f(0) = 02 + 3

= 3

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


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) = `(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


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(3)


If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(0.5)


If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1)


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} > 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.

{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 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:

Find f ° g and g ° f: f(x) = 256x4, g(x) = `sqrt(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

|x2 − 9| + |x2 − 4| = 5


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


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:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

`[x/2] + [x/3] = (5x)/6`


Answer the following:

Find (f ° f) (x) if f(x) = `x/sqrt(1 + x^2)`


If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof 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: ______ 


The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-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)


Given, the function f(x) = `(a^x + a^(-x))/2 (a > 2)`, then f(x + y) + f (x − y) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×