Advertisements
Advertisements
प्रश्न
Find the value of k, such that fog = gof
f(x) = 2x – k, g(x) = 4x + 5
Advertisements
उत्तर
f(x) = 2x – k, g(x) = 4x + 5
fog(x) = f(g(x)) = f(4x + 5) = 2(4x + 5) – k
= 8x + 10 – k …(1)
gof(x) = g(f(x)) = g(2x – k) = 4(2x – k) + 5
= 8x – 4k + 5 ...(2)
(1) = (2)
⇒ 8x + 10 – k = 8x – 4k + 5
3k = – 5
k = `(-5)/(3)`
APPEARS IN
संबंधित प्रश्न
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
Find the value of k, such that fog = gof
f(x) = 3x + 2, g(x) = 6x – k
If f(x) = x2 – 1. Find fof
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 :
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 ______.
For \(f:A\to B\) and \(g:B\to C\), what are the domain and codomain of \(g\circ f\)?
For \(f(x)=4x^2+1\) and \(g(x)=\frac{1}{x+2}\), what is \((g\circ f)(2)\)?
For functions \(f,g,h:\mathbb{R}\to\mathbb{R}\), which identity is established for addition?
For functions \(f,g,h:\mathbb{R}\to\mathbb{R}\), which identity is established for multiplication?
