Question

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

Find f(g(x))

Answer 1

Just replace the x in f(x) with g(x) [that is 2/x]

Answer 2

\[\Large f(g(x)) = f( \frac{2}{x}) = \frac{ \frac{2}{x}}{2}+x\]

Answer 3

understood?

can you continue now?

Answer 4

Its the computation I am having trouble with.

Answer 5

wait sorry!! have a question

Answer 6

Ok

\[\text{You have \to find } \huge f \left( g(x) \right)\]

so its given g(x) = 2/x

so replace g(x) with 2/x\[\huge f \left( g(x) \right) = f \left( \frac{2}{x} \right)\]

is this clear?

Answer 7

When I replace the terms I get 2/x/2+2/x?

Answer 8

Oh Well YES! that was my mistake & i'm extremely sorry about it

Answer 9

no problem, please continue.

Answer 10

\[\large f(x)= \frac{x}{2}+x\]\[\Large f \left( \frac{2}{x} \right) = \frac{\left( \frac{2}{x} \right)}{2}+ \left( \frac{2}{x} \right)\]

Answer 11

are you having any trouble in simplifying it?

Answer 12

yes

Answer 13

tell me what is \(\large \frac{\left( \frac{2}{x} \right)}{2}\)

Answer 14

4x

Answer 15

4/x

Answer 16

i hope you know that 2 can be written as 2/1

so here we are dividing a fraction by another fraction

\[ \large \frac{\left( \frac{2}{x} \right)}{ \left( \frac{2}{1} \right)} \]so here we take reciprocal \[ \large \frac{\left( \frac{2}{x} \right)}{ \left( \frac{2}{1} \right)} = \frac{2}{x} \times \frac{1}{2}\]
so what do you get now?

Answer 17

2/2x

Answer 18

Yes ,what is 2/2x

Answer 19

(2/x)/2

Answer 20

Noo... 2/2x can be simplified

\[\frac{2}{2 \times x} = \frac{\cancel{2}}{\cancel{2} \times x} = ?\](we are cancelling out because 2/2=1)

Answer 21

1/x

Answer 22

Right!!! :D

Now what do you have ?

Answer 23

\[\Large f \left( \frac{2}{x} \right) = \frac{\left( \frac{2}{x} \right)}{2}+ \left( \frac{2}{x} \right) = \frac{1}{x} + \frac{2}{x}\]
Is this clear?

Answer 24

3/x

Answer 25

Very Good! :D

Answer 26

i hope you understood!

Answer 27

yes but my text gives the answer 1/x+1

Answer 28

wait..

is your question
\[f(x)= \frac{x}{2+x}~~~or~~~ f(x)= \frac{x}{2} + x\]

Answer 29

The first.

Answer 30

@Diyadiya

Answer 31

i think its the first one, then you'll get the answer 1/x+1

same way we replace g(x) in f(g(x)) by 2/x

\[\Large f(\frac{2}{x}) = \frac{\left( \frac{2}{x} \right)}{2+\left( \frac{2}{x} \right)}\]

Lets do the denominator first

what is 2 + 2/x ?\[2+\frac{2}{x}~~=~~ \frac{2}{1}+ \frac{2}{x}~~=~~\frac{2 \times x}{1 \times x} + \frac{2}{x} ~~= \frac{2x}{x}+ \frac{2}{x}\]**i multiplied by x inorder to have common denominator without which you cannot add two fractions

Answer 32

yes

Answer 33

\[\Large f(\frac{2}{x})= \frac{\left( \frac{2}{x} \right)}{\frac{2x}{x}+ \frac{2}{x}}= \frac{\left( \frac{2}{x} \right)}{\frac{2x+2}{x}}\]
Now can you take reciprocal ?

Answer 34

2/x*x/2x+2= 2/2x+2?

Answer 35

factor out the 2

Answer 36

Yes :D

Answer 37

:)

Answer 38

there you have the answer :D

Answer 39

thank you

Answer 40

Anytime :)
sorry i misread the question in the beginning

Answer 41

no problem your fantastic.

Answer 42

Haha Thanks