Answered: "How to find (fog)(x) given f(x)=2x−5 and g(x)=x+2?"

Keely Rivers

Answered question

2023-01-09

How to find

(f o g) (x)

given

f (x) = 2 x - 5

and

g (x) = x + 2

Britney Hood

Beginner2023-01-10Added 9 answers

Another perspective is this:
set

g (x) \to y_{1} = x + 2 \dots \dots \dots . . E q u a t i o n (1)

set

f (x) \to y_{2} = 2 x - 5 \dots \dots . . E q u a t i o n (2)

(f o g) (x)

is such that as f is before the g in

(f o g) (x)

so wherever in

f (x)

you see

x

you substitute

y_{1}

That is; you are substituting

E q u a t i o n (1)

into any

x t \hat{i} s \in E q u a t i o n (2)

So:

(f o g) (x) = 2 (y_{1}) - 5

but

y_{1} = x + 2

So:

(f o g) (x) = 2 (x + 2) - 5

(f o g) (x) = 2 x + 4 - 5 = 2 x - 1

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