How do you find (f of g of h) if

Branden Valentine

Branden Valentine

Answered question

2022-01-23

How do you find (f of g of h) if f(x)=x2+1 and h(x)=x1?

Answer & Explanation

Anabelle Miller

Anabelle Miller

Beginner2022-01-24Added 12 answers

Given:
{f(x)=x2+1g(x)=2xh(x)=x1
One way of thinking about these function compositions is to go back and forth between the symbols and verbal descriptions of what the functions do. In our example:
- f takes the square of a number and adds 1;
- g doubles a number;
- h subtracts 1 from a number.
So a verbal description of the composed fgh as a sequence of steps might be:
- Subtract 1;
- Double;
- Square;
- Add 1.
So in symbols we might describe this process thus:
xx12(x1)(2(x1))2(2(x1))2+1
So:
(fgh)(x)=f(g(h(x)))
=(2(x1))2+1
=4(x22x+1)+1
=4x28x+4+1
=4x28x+5

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