मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6

बेरीज

उत्तर

g(x) = x3 − 2x2 − 5x + 6

= (x – 1) (x2 – x – 6)

= (x – 1) (x + 2) (x – 3)

g(x) = 0

∴ (x – 1) (x + 2) (x – 3) = 0

∴ x – 1 = 0 or x + 2 = 0 or x – 3 = 0

∴ x = 1, – 2, 3

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Exercise 6.1 [पृष्ठ ११८]

APPEARS IN

संबंधित प्रश्‍न

If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 1))`


Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:

(a) range of f, i.e. f(A).


Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:

(b) pre-images of 6, −3 and 5.

 

Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?


fgh are three function defined from R to R as follow:

(i) f(x) = x2

Find the range of function.

 

If  \[f\left( x \right) = \begin{cases}x^2 , & \text{ when }  x < 0 \\ x, & \text{ when }  0 \leq x < 1 \\ \frac{1}{x}, & \text{ when }  x \geq 1\end{cases}\]

find: (a) f(1/2), (b) f(−2), (c) f(1), (d)

\[f\left( \sqrt{3} \right)\] and (e) \[f\left( \sqrt{- 3} \right)\]
 

Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] . 


Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.


The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =


Which of the following relations are functions? If it is a function determine its domain and range:

{(1, 1), (3, 1), (5, 2)}


Check if the following relation is a function.


If f(m) = m2 − 3m + 1, find f(0)


If f(m) = m2 − 3m + 1, find f(x + 1)


If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b


An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x2 


Express the following exponential equation in logarithmic form

231 = 23


Prove that alogcb = blogca


Select the correct answer from given alternatives.

Find x, if 2log2 x = 4


Select the correct answer from given alternatives

If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to


Answer the following:

Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph


Answer the following:

Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0


Answer the following:

Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`


Given the function f: x → x2 – 5x + 6, evaluate f(2)


A graph representing the function f(x) is given in it is clear that f(9) = 2

Describe the following Range


If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0


The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.


Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______ 


The domain of the function f(x) = log3+x (x2 - 1) is ______.


Domain of function f(x) = cos–1 6x is ______.


Let f : R → R be defined by 

f(x) = `{(3x;    x > 2),(2x^2;    1 ≤ x ≤ 2), (4x;   x < 1):}`

Then f(-2) + f(1) + f(3) is ______ 


Find the domain of the following function.

f(x) = [x] + x


Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`


Find the domain and range of the function f(x) = `1/sqrt(x - 5)`


The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.


The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×