Advertisements
Advertisements
Question
Find the value of k, such that fog = gof
f(x) = 3x + 2, g(x) = 6x – k
Advertisements
Solution
f(x) = 3x + 2, g(x) = 6x – k
fog(x) = f(g(x))
= f(6x – k)
= 3(6x – k) + 2
= 18x – 3k + 2 …(1)
gof(x) = g(f(x))
= g(3x + 2)
= 6(3x + 2) – k
= 18x + 12 – k ...(2)
(1) = (2)
⇒ 18x – 3k + 2 = 18x + 12 – k
2k = –10
k = –5
APPEARS IN
RELATED QUESTIONS
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = 3 + x, g(x) = x – 4
If f(x) = x2 – 1, g(x) = x – 2 find a, if gof(a) = 1
If f(x) = x2 – 1. Find fof
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
Which statement correctly describes the order of applying functions in \(g\circ f\)?
For \(f(x)=4x^2+1\) and \(g(x)=\frac{1}{x+2}\), what is \((g\circ f)(2)\)?
For \(f(x)=4x^2+1\) and \(g(x)=\frac{1}{x+2}\), which formula represents \((g\circ f)(x)\)?
For \(f(x)=4x^2+1\) and \(g(x)=\frac{1}{x+2}\), which formula represents \((f\circ g)(x)\)?
For \(f(x)=\frac{x-1}{x+1}\), which expression equals \((f\circ f)(x)\)?
