Find the values of x for which the functions

f (x) = 3x² – 1 and g (x) = 3 + x are equal

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)}

Write the following relations as sets of ordered pairs and find which of them are functions:

i. {(x, y): y = 3x, x ∈ {1, 2, 3}, y ∈ {3, 6, 9, 12}}

ii. {(x, y): y > x + 1, x = 1, 2 and y = 2, 4, 6}

iii. {(x, y): x + y = 3, x, y ∈ {0, 1, 2, 3}}

If , where x ≠ –1 and f{f(x)} = x for x ≠ –1 then find the value of k.

Let , then

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

(fg) (x)

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

(f + g) (x)

Express the function f : X → R given by f(x) = x³ + 1 as set of ordered pairs, where X = {–1, 0, 3, 9, 7}.

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g (x) = αx + β, then what values should be assigned to α and β?

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

If f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3, then a and b are equal to