Write its domain and range. Also, draw the graph of f(x). Answer : Given: To Find: Domain and Range of f(x) When f(x) = 1 – x | x < 0 In this case there is no value of x (x < 0) which makes...
Consider the function f: R → R, defined by
read more
Excercise 3C
Find the domain and the range of each of the following real f(x)=1/2 – sin3x function:
Answer : Given: Need to find: Where the functions are defined. The maximum value of an angle is 2π So, the maximum value of x = 2π/3. Whereas, the minimum value of x is 0 Therefore, the domain of...
Find the domain and the range of each of the following real f(x)=x-9/x-3 function:
Answer : Given: Need to find: Where the functions are defined. To find the domain of the function f(x) we need to equate the denominator of the function to 0. Therefore, x – 3 = 0 ⇒ x = 3 It means...
Find the domain and the range of each of the following real f(x)=|x-4|/x-4 function:
Answer : Given: Need to find: Where the functions are defined. To find the domain of the function f(x) we need to equate the denominator of the function to 0. Therefore, x – 4 = 0 ⇒ x = 4 It means...
Find the domain and the range of each of the following real function: f(x) = 1 – |x – 2|
Answer : Given: f(x) = 1 – |x – 2| Need to find: Where the functions are defined. Since |x – 2| gives real no. for all values of x, the domain set can possess any real numbers. So, the domain of the...
Find the domain and the range of each of the following real function: f(x)=ax-b/cx-d
Answer : Given: f(x) = ax-b/cx-d Need to find: Where the functions are defined. Let,---------------------------- (1) To find the domain of the function f(x) we need to equate the denominator of the...
Find the domain and the range of each of the following real f(x)=x-16/x-4 function:
Answer : Given: Need to find: Where the functions are defined. To find the domain of the function f(x) we need to equate the denominator of the function to 0. Therefore, x – 4 = 0 ⇒ x = 4 It means...
Find the domain and the range of each of the following real f(x)=3x-2/x+2
Answer : Given: Need to find: Where the functions are defined. Let,--------------------------- (1) To find the domain of the function f(x) we need to equate the denominator of the function to 0....
Find the domain and the range of each of the following real f(x)=x-3/2-x
Answer : Given: Need to find: Where the functions are defined. Let,-------------------------- (1) To find the domain of the function f(x) we need to equate the denominator of the function to 0....
Find the domain and the range of each of the following real f(x)=1/x-5 function:
Answer : Given: Need to find: Where the functions are defined. Let,-------------------------- (1) To find the domain of the function f(x) we need to equate the denominator of the function to 0....
Find the domain and the range of each of the following real function: f(x)=1/x
Answer : Given: Need to find: Where the functions are defined. Let,----------------------- (1) To find the domain of the function f(x) we need to equate the denominator of the function to 0....
Find the domain of each of the following real function.
Answer : (i) Given: Need to find: Where the functions are defined. It means that the denominator is zero when x = 3 and x = -3 To find the domain of the function f(x) we need to equate the...
Solve the system of equations by using the method of cross multiplication:
,
, where 
and 
Solution: On substituting $\frac{1}{x}=u$ and $\frac{1}{y}=v$ in the equations given, we obtain $\mathrm{au}-\mathrm{bv}+0=0$ $a b^{2} u+a^{2} b v-\left(a^{2}+b^{2}\right)=0$ Here, $a_{1}=a,...
Solve the system of equations by using the method of cross multiplication:
Solution: We can write the given equation as: $\begin{array}{l} 2 a x+3 b y-(a+2 b)=0\dots \dots(i) \\ 3 a x+2 b y-(2 a+b)=0\dots \dots(i) \end{array}$ Here, $a_{1}=2 \mathrm{a}, \mathrm{b}_{1}=3...
Solve the system of equations by using the method of cross multiplication:
,
Solution: We can write the given equations as: $\begin{array}{l} \frac{a x}{b}-\frac{b y}{a}-(a+b)=0\dots \dots(i) \\ a x-b y-2 a b=0\dots \dots(ii) \end{array}$ Here, $a_{1}=\frac{a}{b},...
Solve the system of equations by using the method of cross multiplication:
,
Solution: Taking $\frac{1}{x+y}=u$ and $\frac{1}{x-y}=v$, the given equations become: $5 u-2 v+1=0\dots \dots(i)$ $15 u+7 v-10=0 \quad \ldots \ldots($ ii $)$ Here, $\mathrm{a}_{1}=5,...
Solve the system of equations by using the method of cross multiplication:
,
Solution: Taking $\frac{1}{x}=u$ and $\frac{1}{y}=v$, the given equations become: $\begin{array}{l} \mathrm{u}+\mathrm{v}=7 \\ 2 \mathrm{u}+3 \mathrm{v}=17 \end{array}$ We can write the given...
Solve the system of equations by using the method of cross multiplication:
,
Solution: The given equations may be written as: $\begin{array}{l} \frac{x}{6}+\frac{y}{15}-4=0\dots \dots(i) \\ \frac{x}{3}-\frac{y}{12}-\frac{19}{4}=0\dots \dots(ii) \end{array}$ Here...
Solve the system of equations by using the method of cross multiplication:
Solution: The given equations may be written as: $\begin{array}{l} 7 x-2 y-3=0\dots \dots(i) \\ 11 x-\frac{3}{2} y-8=0\dots \dots(ii) \end{array}$ Here $a_{1}=7, b_{1}=-2, c_{1}=-3, a_{2}=11,...
Solve the system of equations by using the method of cross multiplication:
Solution: The given equations are: $\begin{array}{ll} 3 \mathrm{x}-2 \mathrm{y}+3=0 & \ldots \ldots (i)\\ 4 \mathrm{x}+3 \mathrm{y}-47=0 & \ldots \ldots (ii) \end{array}$ Here $a_{1}=3,...
Solve the system of equations by using the method of cross multiplication:
Solution: The given equations are: $\begin{array}{l} x+2 y+1=0\dots \dots (i) \\ 2 x-3 y-12=0\dots \dots(ii) \end{array}$ Here $a_{1}=1, b_{1}=2, c_{1}=1, a_{2}=2, b_{2}=-3$ and $c_{2}=-12$ On cross...