Let A = R – {2}, B = R – {1}. If f : A → B is a function defined by show that f is one-one and onto. Hence find
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).
Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) = find gof(x) .
Find the equation of tangent to the curve x² + 3y = 3, which is parallel to line y – 4x + 5 = 0.
Find a vector of magnitude 5 units and parallel to the resultant of = and = .
Find the position vector of a point R, which divides the line joining two points P and Q whose position vectors are and respectively, externally in the ratio 1 : 2 Also, show that P is the mid-point, of line segment RQ.
Show that the function f in A = defined as f(x) = is one-one and onto. Hence find