If f(x) = (1 − x)^2 and g(x) = 9 − x,

 find f(g(x)) and g(f(x)). 

 Apr 25, 2020

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...... cheeky

 Apr 25, 2020

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


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    laugh

Melody  Apr 28, 2020

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