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
Show that a function f : R → R given by f(x) =ax + b,a, b ∈ R, a ≠ 0 is a bijective.
Show that the function f : R {x ∈ R – 1 < x < 1} defined by f(x) = x ∈ R is one-one and onto function. Hence find f⁻¹(x).
Show that f : N → N, given by f(x) = |``x+1, if x is odd x- 1, if x is even is both one-one and onto.``|
If the function f : R → R be given by f(x) = x² + 2 and g : R → R be given by g(x) = find fog and gof and hence find fog(2) and gof(– 3).
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).
Find the equations of tangents to the curve y = (x²– 1) (x – 2) at the points, where the curve cuts the X-axis.
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Find a vector of magnitude 5 units and parallel to the resultant of = and = .