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# Functions and Modeling

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If f(x) = (1 − x)^2 and g(x) = 9 − x,

find f(g(x)) and g(f(x)).

Apr 25, 2020

#1
+28025
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f(g(x))      put in g(x) which is  9-x  in for 'x' in the definition of f(x)

(1-x)^2     put in  9-x   for 'x'

(1 -   (9-x)) ^2

= (x -8)^2   =      x^2 -16x+64

You should be able to do the other one now......

Apr 25, 2020
#2
+115
+1

thanks. I am getting confused on the second one because in the problem you did, you subtracted the 1-9. In the second problem I tried doing that same thing. It was incorrect. 9-(1-x)^2= (8-x)^2 =x^2+16x+64 that was incorrect. I guess Im wondering where I went wrong?

Shaezy  Apr 27, 2020
#3
+111978
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Hi Shaezy,

It is good to see you interacting here.

Your substitution is perfect, EP taught you well,  it is your simplifying that is incorrect.

$$If \;\;f(x) = (1 − x)^2 \qquad g(x) = 9 − x,\\ find\;\; f(g(x)) \;\;and ;\;g(f(x)). \\\\~\\ g(f(x))= 9-(1-x)^2$$

So far so good.  BUT

$$\text{This is NOT }(8-x)^2\\ \text{it is } \quad9-[(1-x)^2]$$

You have to expand the bracket and then take away ALL the terms from 9.

Have another go at it

Melody  Apr 28, 2020