Advertisements
Advertisements
Question
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = x – 6, g(x) = x2
Advertisements
Solution
f(x) = x – 6, g(x) = x2
fog = fog(x)
= f(g(x))
fog = f(x)2
= x2 – 6
gof = gof(x)
= g(x – 6)
= (x – 6)2
= x2 – 12x + 36
fog ≠ gof
APPEARS IN
RELATED QUESTIONS
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) = `(x + 6)/3`, g(x) = 3 – x
If f(x) = 2x – 1, g(x) = `(x + 1)/(2)`, show that fog = gof = x
If f(x) = x2 – 1. Find fofof
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?
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
Multiple choice question :
If g = {(1, 1), (2, 3), (3, 5), (4, 7)} is a function given by g(x) = αx + β then the value of α and β are
Given f(x) = log `((1 + x)/(1 − x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals ______.
