Advertisements
Advertisements
Question
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = `(2)/x`, g(x) = 2x2 – 1
Advertisements
Solution
f(x) = `(2)/x`, g(x) = 2x2 – 1
fog = f[g(x)]
= f(2x2 – 1)
= `(2)/(2x^2 - 1)`
gof = g[f(x)]
= `g(2/x)`
= `2(2/x)^2 - 1`
= `2 xx 4/x^2 - 1`
= `8/x^2 - 1`
fog ≠ gof
APPEARS IN
RELATED QUESTIONS
Find k, if f(k) = 2k – 1 and fof(k) = 5
If f(x) = x2 – 1. Find fof
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?
Multiple choice question :
If f(x) = 2x2 and g(x) = `1/(3x)`, then 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
If f(x)= x2, g(x) = 3x and h(x) = x – 2 Prove that (fog)oh = fo(goh)
If three functions are composable, which associative property holds?
For \(f(x)=4x^2+1\) and \(g(x)=\frac{1}{x+2}\), which formula represents \((g\circ f)(x)\)?
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?
