English

Answer the following: Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph - Mathematics and Statistics

Advertisements
Advertisements

Question

Answer the following:

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

Graph
Sum

Solution

Let y = f(x) = x3 + 1

x –2 –1 0 1 2
–7 0 1 2 9

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Functions - Miscellaneous Exercise 6.2 [Page 131]

APPEARS IN

RELATED QUESTIONS

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

 

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

(i) \[f\left( \frac{1}{x} \right) = - f\left( x \right)\]

(ii) \[f\left( - \frac{1}{x} \right) = - \frac{1}{f\left( x \right)}\]


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

 

If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to

 

If  \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . 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 \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is

 

The range of the function f(x) = |x − 1| is


Check if the following relation is function:


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)}


Find the domain and range of the following function.

g(x) = `(x + 4)/(x - 2)`


Express the following exponential equation in logarithmic form

3–4 = `1/81`


Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2


Find the domain of f(x) = ln (x − 5)


Write the following expression as sum or difference of logarithm

In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`


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


Prove that `"b"^(log_"b""a"` = a


Prove that logbm a = `1/"m" log_"b""a"`


Solve for x.

2 log10 x = `1 + log_10 (x + 11/10)`


If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7


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


Select the correct answer from given alternatives.

If f(x) =`1/(1 - x)`, then f{f[f(x)]} is


Answer the following:

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


Answer the following:

Show that, logy x3 . logz y4 . logx z5 = 60


Answer the following:

If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k


Answer the following:

Find the domain of the following function.

f(x) = 5–xPx–1


Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?


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

Find the following values of the function 

(a) f(0)

(b) f(7)

(c) f(2)

(d) f(10)


A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0


A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2


The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Length ‘x’ of
forehand (in cm)
Height 'y' 
(in inches)
35 56
45 65
50 69.5
55 74

Find the length of forehand of a person if the height is 53.3 inches


Find the range of the following functions given by `sqrt(16 - x^2)`


If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.


Find the range of the following functions given by f(x) = 1 – |x – 2| 


Let f(x) = `sqrt(1 + x^2)`, then ______.


The ratio `(2^(log_2  1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×