Given connection \[R\text{ }=\text{ }\left\{ \left( a,\text{ }b \right):\text{ }a,\text{ }b\in N\text{ }and\text{ }a\text{ }=\text{ }b2 \right\}\] (iii) Its unmistakably seen that \[\left( 16,\text{...
Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (i) (a, a) ∈ R, for all a ∈ N (ii) (a, b) ∈ R, implies (b, a) ∈ R
Given connection \[R\text{ }=\text{ }\left\{ \left( a,\text{ }b \right):\text{ }a,\text{ }b\in N\text{ }and\text{ }a\text{ }=\text{ }b2 \right\}\] (I) It can be seen that 2 ∈ N; nonetheless, 2 ≠ 22...
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B.
Given, \[A\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4 \right\}\text{ }and\text{ }B\text{ }=\text{ }\left\{ 1,\text{ }5,\text{ }9,\text{ }11,\text{ }15,\text{ }16 \right\}\] Thus,...
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
Given connection f is characterized as \[f\text{ }=\text{ }\left\{ \left( ab,\text{ }a\text{ }+\text{ }b \right):\text{ }a,\text{ }b\in Z \right\}\] We realize that a connection f from a set A to a...
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
Given, \[A\text{ }=\text{ }\left\{ 9,\text{ }10,\text{ }11,\text{ }12,\text{ }13 \right\}\] Presently, f: A → N is characterized as f(n) = The most elevated prime factor of n Thus, Prime factor of 9...
Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
Given, \[f\text{ }=\text{ }\left\{ \left( 1,\text{ }1 \right),\text{ }\left( 2,\text{ }3 \right),\text{ }\left( 0,\text{ }\text{ }1 \right),\text{ }\left( \text{ }1,\text{ }\text{ }3 \right)...
Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f/g.
Given, the capacities f, g: R → R is characterized as \[f\left( x \right)\text{ }=\text{ }x\text{ }+\text{ }1,\text{ }g\left( x \right)\text{ }=\text{ }2x\text{ }\text{ }3\] Presently, \[\left(...
Let F=(FIG 1) be a function from R into R. Determine the range of f.
FIG 1: SOLUTION: Given capacity, Subbing esteems and deciding the pictures, we have The scope of f is the arrangement of the entire second components. It tends to be seen that this load of...
Find the domain and the range of the real function f defined by f (x) = |x – 1|.
Given genuine capacity, \[f\text{ }\left( x \right)\text{ }=\text{ }\left| x\text{ }\text{ }1 \right|\] Unmistakably, the capacity \[\left| x\text{ }\text{ }1 \right|\] is characterized for all...
Find the domain and the range of the real function f defined by f(x) = √(x – 1).Find the domain and the range of the real function f defined by f(x) = √(x – 1).
Given genuine capacity, \[f\left( x \right)\text{ }=\text{ }\surd \left( x\text{ }\text{ }1 \right)\] Plainly, √(x – 1) is characterized for \[\left( x\text{ }\text{ }1 \right)\text{ }\ge \text{...
Find the domain of the function f(x):
SOLUTION: Given capacity, It obviously seen that, the capacity f is characterized for all genuine numbers besides at \[x\text{ }=\text{ }6\] and \[x\text{ }=\text{ }2\] as the denominator becomes...
If f(x) = x2, find (FIG1)
FIG 1: SOLUTION: Given, \[f\left( x \right)\text{ }=\text{ }x2\] Thus,
The relation f is defined by (FIG 1) The relation g is defined by(FIG 2).Show that f is a function and g is not a function.
FIG 1: FIG 2: SOLUTION: The given connection f is characterized as: It is seen that, for\[0\text{ }\le \text{ }x\text{ }<\text{ }3\] , \[f\left( x \right)\text{ }=\text{ }x2\text{ }and\text{...