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.``|
Show that a function f : R → R given by f(x) =ax + b,a, b ∈ R, a ≠ 0 is a bijective.
Prove that the function f : [0, ∞) → R given by f(x) = 9x² + 6x – 5 is not invertible. Modify the Codomain of the function f to make it invertible, and hence find f⁻¹.
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).
Consider given by f(x) = Show that f is bijective. Find the inverse of f and hence find f⁻¹(0) and x such that f⁻¹(x) = 2.
Consider given by f(x) = 5x² + 6x – 9.Prove that f is invertible with f⁻¹(y) = [where, R⁺ is the set of all nonnegative real numbers.]
Show that the function f:R → R defined by f(x) = is neither one-one nor onto. Also,
if g:R → R is defined as g(x) = 2x – 1, find fog(x).
Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) = 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)].
Write fog, if f : R → R and g : R → R are given by f(x) = 8x³ and g(x) =
If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)
Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.
If f(x) = 27x³ and g(x) = , then find gof(x).
If f : R → R is defined by f(x) = then find fof(x).