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

If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)

बेरीज

उत्तर

f(x) = 3x + 5, g(x) = 6x − 1

f(2) = 3(2) + 5 = 11

g(2) = 6(2) - 1 = 11

∴ (f − g) (2) = f(2) − g(2)

= 11 − 11

= 0.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Exercise 6.2 [पृष्ठ १२७]

APPEARS IN

संबंधित प्रश्‍न

Find the domain of the function  f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`


\[f\left( x \right) = \begin{cases}3x - 2, & x < 0; \\ 1, & x = 0; \\ 4x + 1, & x > 0 .\end{cases}\]

find: f(1), f(−1), f(0) and f(2).

 

 


Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(b) {x : f(x) = −2}


If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].

 

If  \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.

 

 


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) \[f\left( \sqrt{- 3} \right)\]
 

If  \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that

\[f\left( x \right) + f\left( \frac{1}{x} \right) = 0 .\]
 

 


If f(x) = (a − xn)1/na > 0 and n ∈ N, then prove that f(f(x)) = x for all x.

 

Let f and g be two functions given by

f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.

Find the domain of f + g


The range of  \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is 

 


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

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


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

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


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


Find the domain and range of the follwoing function.

h(x) = `sqrt(x + 5)/(5 + x)`


Find the domain and range of the following function.

f(x) = `root(3)(x + 1)`


Find the domain and range of the following function.

f(x) = `sqrt((x - 2)(5 - x)`


Express the following exponential equation in logarithmic form

54° = 1


Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b


If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b


Select the correct answer from given alternatives.

If log (5x – 9) – log (x + 3) = log 2 then x = ...............


The equation logx2 16 + log2x 64 = 3 has,


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:

A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist


Answer the following:

Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not


Answer the following:

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


Answer the following:

Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph


Answer the following:

Solve for x, logx (8x – 3) – logx 4 = 2


Answer the following:

Find the domain of the following function.

f(x) = 5–xPx–1


Find the domain of the following function.

f(x) = `sqrtlog(x^2 - 6x + 6)`


Answer the following:

Find the range of the following function.

f(x) = [x] – x


The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`

 Calculate the value of `"gg" (1/2)`


Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x3 then, find the range of f


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


If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.


Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3


Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find `(f/g)(x)`


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


The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×