Find gof and fog when f: R → R and g: R → R is defined by f(x) = 2x+3 and g(x) = x^2 +5 Watch Solution
Find gof and fog when f: R → R and g: R → R is defined by f(x) = 2x + x^2 and g(x) = x^3 Watch Solution
Find gof and fog when f: R → R and g: R → R is defined by f(x) = x^2 + 8 and g(x) = 3x^3 + 1 Watch Solution
Find gof and fog when f: R → R and g: R → R is defined by f(x) = x and g(x) = |x| Watch Solution
Find gof and fog when f: R → R and g: R → R is defined by f(x) = x^2 + 2x – 3 and g(x) = 3x – 4 Watch Solution
Find gof and fog when f: R → R and g: R → R is defined by f(x) = 8x^3 and g(x) = x^1/3 Watch Solution
Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5, 9)}. Show that gof and fog are both defined, Also, find fog and gof. Watch Solution
Let f = {(1, – 1), (4, – 2), (9, – 3), (16, 4)} and g = {(- 1, – 2), (- 2, – 4), (- 3, – 6), (4, 8)}. Show that gof is defined while fog is not defined. Also, find gof. Watch Solution
Let A = {a, b c}, B = {u, v, w} and let f and g be two functions from A to B and from B to A respectively defined as: f = {(a, v), (b, u), (c, w)}, g = {(u, b), (v, a), (w, c)}. Watch Solution
Find fog (2) and gof (1) when: f: R → R; f(x) = x^2 + 8 and g: R → R; g(x) = 3x^3 + 1 Watch Solution
Let R+ be the set of all non – negative real numbers. If f: R+→ R+ and g: R+→ R+ are defined as f(x) =x^{2} and g(x) = + √x. Find fog and gof. Are they equal functions. Watch Solution
Let f: R → R and g: R → R be defined by f(x) = x^2 and g(x) = x + 1. Show that fog ≠ gof. Watch Solution
Let f: R → R an g: R → R be defined by f(x) = x + 1 and g(x) = x – 1. Show that fog = gof = IR Watch Solution
Verify associativity for the following three mappings: f: N → Z0 (the set of non – zero integers), g: Z0→ Q and h: Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = e^{x} Watch Solution
Consider f: N → N, g: N → N and h: N → R defined as f(x) = 2x, g(y) = 3y + 4 and h(z) = sin z for all x, y, z ∈ N. Show that ho (gof) = (hog) of. Watch Solution
Give examples of two functions f: N → N and g: N → N such that gof is onto, but f is not onto. Watch Solution
Give examples of two functions f: N → Z and g: Z → Z such that gof is injective, but g is not injective. Watch Solution
If f: A → B and g: B → C are one-one functions show that gof is a one-one function. Watch Solution
If f: A → B and g: B → C are onto functions show that gof is an onto function. Watch Solution
