हिंदी

If f(m) = m2 − 3m + 1, find f(12) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If f(m) = m2 − 3m + 1, find `f(1/2)`

योग

उत्तर

f(m) = m2 – 3m + 1

`f(1/2) = (1/2)^2 - 3(1/2) + 1`

= `1/4 - 3/2 + 1` 

= `(1 - 6 + 4)/4`

= `(5 - 6)/4`

= `-1/4`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Exercise 6.1 [पृष्ठ ११८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.1 | Q 4. (c) | पृष्ठ ११८

संबंधित प्रश्न

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

  1. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
  2. {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
  3. {(1, 3), (1, 5), (2, 5)}

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 X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.

(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)} 


If for non-zero xaf(x) + bf \[\left( \frac{1}{x} \right) = \frac{1}{x} - 5\] , where a ≠ b, then find f(x).

 

Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function: 

(ii) g − 


If f(x) = loge (1 − x) and g(x) = [x], then determine function:

(iii) \[\frac{f}{g}\]

 

Write the range of the function f(x) = ex[x]x ∈ R.

 

Write the domain and range of function f(x) given by

\[f\left( x \right) = \frac{1}{\sqrt{x - \left| x \right|}}\] .
 

Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.


If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is 


If f(x) = sin [π2x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then


The domain of definition of the function  \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is

 

The domain of definition of  \[f\left( x \right) = \sqrt{4x - x^2}\] is 

 

The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is


Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 2), (2, −1), (3, 1), (4, 3)}


Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 1), (2, 1), (3, 1), (4, 1)}


If f(m) = m2 − 3m + 1, find f(x + 1)


Find the domain and range of the following function.

f(x) = `sqrt(16 - x^2)`


Check the injectivity and surjectivity of the following function.

f : N → N given by f(x) = x2 


Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2


Express the following logarithmic equation in exponential form

`log_(1/2) (8)` = – 3


Find the domain of f(x) = ln (x − 5)


Find the domain of f(x) = log10 (x2 − 5x + 6)


If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)


Select the correct answer from given alternatives.

If log10(log10(log10x)) = 0 then x =


Select the correct answer from given alternative.

The domain and range of f(x) = 2 − |x − 5| is


Answer the following:

Find whether the following function is one-one

f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}


Answer the following:

Let f: R → R be a function defined by f(x) = 5x3 – 8 for all x ∈ R, show that f is one-one and onto. Hence find f –1 


Answer the following:

If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b


Answer the following:

Find the range of the following function.

f(x) = `x/(9 + x^2)`


Answer the following:

Find the range of the following function.

f(x) = [x] – x


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

 Describe the following Domain


If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.


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


Find the range of the following functions given by f(x) = 1 + 3 cos2x

(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)


The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.


The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.


If f(x) = `log_e{((1 - x))/((1 - x))}, |x| < 1, f{(2x)/((1 + x^2))}` is equal to ______.


Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×