Advertisements
Advertisements
प्रश्न
If f : R → R and g : R → R are defined by f(x) = x5 and g(x) = x4 then check if f, g are one-one and fog is one-one?
Advertisements
उत्तर
f(x) = x5 – It is one-one function
g(x) = x4 – It is one-one function
fog = fog[g(x)] = f[g(x)]
= f(x4)
= (x4)5
fog = x20
f is one-one, g is not one-one.
∵ g(1) = 14 = 1
g(-1) = (-1)4 = 1
Different elements have same images
fog is not one-one. [∵ fog (1) = fog (-1) = 1]
APPEARS IN
संबंधित प्रश्न
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = x – 6, g(x) = x2
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = `(2)/x`, g(x) = 2x2 – 1
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = 4x2 – 1, g(x) = 1 + x
Find the value of k, such that fog = gof
f(x) = 3x + 2, g(x) = 6x – k
If f(x) = 2x – 1, g(x) = `(x + 1)/(2)`, show that fog = gof = x
Find k, if f(k) = 2k – 1 and fof(k) = 5
Consider the function f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)
f(x) = x2, g(x) = 2x and h(x) = x + 4
Consider the function f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)
f(x) = x – 4, g(x) = x2 and h(x) = 3x – 5
Multiple choice question :
Let f and g be two function given by f = {(0, 1), (2, 0), (3, – 4), (4, 2), (5, 7)} g = {(0, 2), (1, 0), (2, 4), (– 4, 2), (7, 0) then the range of fog is
If f(x)= x2, g(x) = 3x and h(x) = x – 2 Prove that (fog)oh = fo(goh)
