201k views
1 vote
F(x)=x^ 2 +x-6;g(x)=x-2 need help with this

2 Answers

4 votes

two functions f(x) and g(x) are called inverse of each other when these follow this rule.

if we put x in f we get the value f(x)

then putting f(x) in g should give us the value x

in other words

let's say I put x = a in f(x) we get f(a)

now when we will put x = f(a) in g(x) we should get a back.

then they called inverse of each other.

let's take an example

f(x) = 4x-2

g(x) = (x+2)/4

let's put x = 1 in f(x)

f(1) = 4×1-2 = 4-2 = 2

f(1)= 2

now we will put 2 in g(x) and it should give us value 1

g(f(1))= g(2) =(2+2)/4= 4/4 = 1

yes we got 1. doing same in reverse order . that is we will check now g(x) first.

lets take x= -2 for simplification

g(-2) = (-2+2)/4 = 0

now f(0) = 4×0-2 = -2

yes we got it again so in this case functions are inverse to each other.

mathematically

g(f(x)) = x = f(g(x))

let's prove that if above function follows this or not .

f(x) = 2/x - 6

g(x) = 6x + 2/x

let's calculate g(f(x)) first

g(f(x)) = g(2/x -6) = 6(2/x -6) + 2/(2/x -6)

= 12/x -36 + 2x/(2-6x)

which is not equal to x so we don't have to proceed further. they are not inverse of each other

User Evgeny Ruban
by
7.8k points
5 votes

Answer:

hcsiuhdiufhcukehdfkva

Explanation:

User Showtime
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories