English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

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

f(– 4) = 4(– 4) – 2

= – 16 – 2

= – 18

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


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) = `(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


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(– 3)


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(2)


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| ≥ 5


Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

{x} = 0


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) = 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 − 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

[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:

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(x) if g(x) = `1 + sqrt(x)` and f[g(x)] = `3 + 2sqrt(x) + x`


Answer the following:

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


Answer the following:

Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`


The inverse of the function y = `(16^x - 16^-x)/(16^x + 16^-x)` is


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


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


If f(x) =bx - 7 and f(-1) = 4, then b = ______.


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 ______.


`int_0^3 [x]dx` = ______, where [x] is greatest integer function.


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×