Let f, g : R → R be two functions defined as f (x) = |x| + x and g (x) = |x| – x for all x ∈ R.Then find fog and gof.

If the function f : R → R be given by f(x) = x² + 2 and g : R → R be given by g(x) = ${\frac{x}{x-1}},x\neq1,$ find fog and gof and hence find fog(2) and gof(– 3).

If f(x) =$\frac{4x+3}{6x-4}\,,\;\;x\;\;\neq\;\;\frac{2}{3}\,,$ then Show that fof(x) = x for all $x\neq{\frac{2}{3}}\,.$ What is the inverse of f?

Let f : N → R be a function defined as f(x) = 4x² + 12x + 15. Then show that f : N → S, where S is range of f, is invertible. Also find the inverse of f.

If the function f : R → R be defined by f(x) = 2x – 3 and g : R → R by g(x) = x³ + 5, then find fog and show that fog is invertible. Also, find (fog)⁻¹, hence find (fog)⁻¹(9).

If the function f : R → R is given by f(x) = $\frac{x+3}{3}$ and g : R → R is given by g(x) = 2x – 3, then find (i) fog (ii) gof Is f⁻¹ = g?

If the function f : R → R is given by f(x) = x² + 3x + 1 and g : R → R is given by g(x) = 2x – 3, then find (i) fog (ii) gof