If R = {(x, y) : x + 2y = 8} is a relation on N, writethe range of R.

Let R={(a,a³): a is a prime number less than 5} be a relation. Find the range of R.

Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].

State the reason why the Relation R = {(a, b) : a ≤ b²} on the set R of real numbers is not reflexive.

Let A = {1, 2, 3, 4}. Let R be the equivalence relation on A × A defined by (a, b)R(c, d) if a + d = b + c. Find the equivalence class [(1,3)].

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

If f : R → R defined as f(x) =${\frac{2x-7}{4}}\ $ is an invertible function, write $f^{-1}(x).$

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5),(3, 6)} is a function from A to B. State whether f is one-one or not.

If f is an invertible function, defined as f(x) = $\frac{3x-4}{5}$, then write $f^{-1}(x).$

What is the range of the function f(x) = $\textstyle{\frac{|x-1|}{x-1}}$, x ≠ 1?

If the function f : R → R defined by f(x) = 3x - 4 is invertible, then find $f^{-1}.$

If f : R→ R defined by f(x) = $\textstyle{\frac{3x+5}{2}}$ is an invertible function, then find $f^{-1}(x).$

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].