Express As Composite Functions

[mathxyz]

1) Express the function in the form f of g.

F(x) = (x - 9)^5

Express the function as f of g of h.

2) H(x) = 1 - 3^(x^2) READ: 1 minus 3 raised to x squared.

I am confused in terms of the capital F and H letters. I usually see a lower case f and h before (x).

 

[pka]

To do the question we must know the definitions of f, g, h.
You should have been given f(x), g(x) & h(x).
Please post those definitions.

 

[soroban]

Hello, mathxyz!

I think I understand what is being asked.
They want us to break up the given function into two or three smaller functions.

1) Express the function in the form f of g.

F(x) = (x - 9)⁵
.

Let g(x) = x - 9 .and .f(x) = x²

Then: . F(x) .= .f(g(x)) .= .(x - 9)⁵

Express the function as f of g of h.

2) H(x) = 1 - 3^x²

.

Let h(x) = x², . g(x) = 3^x, . f(x) = 1 - x

Then: . H(x) .= .f(g(h(x))) .= . 1 - 3^x²
.


To pka: don't blush . . . I already did ... for the both of us.
I was getting a cup of coffee, thinking "What a stupid problem!" when I saw what it meant.
[I ran cold water on my hand and wiped up the area.]
I'd seen problem like this before . . . I just didn't recognize it.

 

[mathxyz]

Yes

To pka:

Sorry about not posting the entire question.

To Soroban:

You got it!

 

[Guest]

To pka:

Sorry about not posting the entire question.

To Soroban:

You got it!

Wait, was it the entire question or not?

 

[mathxyz]

Yes...

Soroban got it.