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If f (x) = x2, find the value of .
Given: f(x) = x2
To find: …(i)
Firstly, we find the f(5)
Putting the value of x = 5 in the given eq., we get
f(5) = (5)2
⇒ f(5) = 25
Similarly,
f(1) = (1)2
⇒ f(1) = 1
Putting the value of f(5) and f(1) in eq. (i), we get
Hence, the value of
Define a function as a set of ordered pairs.
Define a function as a correspondence between two sets.
What is the fundamental difference between a relation and function? Is every relation a function?
Let X = {1, 2, 3, 4,}, Y = {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 X to Y (ii) F is a function from X to Y. Justify your answer in following true?
Let X = {-1, 0, 3, 7, 9} and f : X → R : f(x) x3 + 1. Express the function f as set of ordered pairs.
Let A = {–1, 0, 1, 2} and B = {2, 3, 4, 5}. Find which of the following are function from A to B. Give reason.
(i) f = {(–1, 2), (-1, 3), (0, 4), 1,5)}
(ii) g = {(0, 2), (1, 3), (2, 4)}
(iii) h = {(-1, 2), (0, 3), (1, 4), (2, 5)}
Let A = {1, 2} and B = {2, 4, 6}. Let f = {(x, y) : x ϵ A, y ϵ B and y > 2x + 1}. Write f as a set of ordered pairs. Show that f is a relation but not a function from A to B.
Let A = {0, 1, 2} and B = {3, 5, 7, 9}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x + 3}. Write f as a set of ordered pairs. Show that f is function from A to B. Find dom (f) and range (f).
Let A = {2, 3, 5, 7} and B = {3, 5, 9, 13, 15}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x – 1}. Write f in roster form. Show that f is a function from A to B. Find the domain and range of f.
Let g = {(1, 2), (2, 5), (3, 8), (4, 10), (5, 12), (6, 12)}. Is g a function? If yes, its domain range. If no, give reason.
Let f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a linear function from Z into Z. Write an expression for f.
If f(x) = x2, find the value of .
Let X = {12, 13, 14, 15, 16, 17} and f : A → Z : f(x) = highest prime factor of x. Find range (f)
Let R+ be the set of all positive real numbers. Let f : R+→ R : f(x) = logex. Find
(i) range (f)
(ii) {x : x ϵ R+ and f(x) = -2}.
(iii) Find out whether f(x + y) = f(x). f(y) for all x, y ϵ R.
Let f : R → R : f(x) =2x. Find
(ii) {x : f(x) = 1}.
Let f : R → R : f(x) =x2 and g : C → C: g(x) =x2, where C is the set of all complex numbers. Show that f ≠ g.
f, g and h are three functions defined from R to R as following:
(i) f(x) = x2
(ii) g(x) = x2 + 1
(iii) h(x) = sin x
That, find the range of each function.
Let f : R → R : f(x) = x2 + 1. Find
(i) f–1 {10}
(ii) f–1 {–3}.
The function is the formula to convert x °C to Fahrenheit units. Find
(i) F(0),
(ii) F(–10),
(iii) The value of x when f(x) = 212.
Interpret the result in each case.