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Problems with Math

Hi everyone:smile:

I am struggling to do some exercises on my math website. They do not have the answers :frown:
Could anyone of you help me with these problems?

http://gyazo.com/b548e8425832cc83606b001bab0473e9

Thank you :smile:
Reply 1
Avatar for Hasufel
Hasufel
16
i`ll do the first one so you can see what they`re after:

the first one is asking you to take the output from f(x) and make that the input to g(x). - i.e. so you have g(4x)=2(4x)−3g(4x)=2^{(4x)-3}

(think of it as g(X)g(X) where X =f(x) )
(edited 10 years ago)
Reply 2
Avatar for beatrice15
beatrice15
OP
On the website this is the only one I got right. I am not sure how to do the second and third one. I was thinking for the second one 23x-9 I don't know sure how to get the right answer.:frown:


Original post by Hasufel
i`ll do the first one so you can see what they`re after:

the first one is asking you to take the output from f(x) and make that the input to g(x). - i.e. so you have g(4x)=2(4x)−3g(4x)=2^{(4x)-3}

(think of it as g(X)g(X) where X =f(x) )
Reply 3
Avatar for Hasufel
Hasufel
16
for the first one f(x)=4xf(x)=4x so, f(g(x))=4(g(x))f(g(x))=4(g(x)) and we just replace g(x) with 2x−32^{x-3} giving: 4×2x−3=22×2x−3=2x−3+2=2x−14 \times 2^{x-3}=2^{2} \times 2^{x-3}=2^{x-3+2}=2^{x-1}

h(g(x)) is a little trickier:


Unparseable latex formula:

\diaplaystyle h(x)=\frac{1}{2x}

so,
Unparseable latex formula:

\diaplaystyle h(g(x))=\frac{1}{2(g(x))}

and we just replace g(x) with 2x−32^{x-3} giving:
Unparseable latex formula:

\diaplaystyle h(g(x))= \frac{1}{2 ( 2^{x-3})}= \frac{1}{2^{x-2}}= \frac{1}{2^{-(2-x)}}=2^{2-x}



You try the others...(same principle - you want 2^(something))
(edited 10 years ago)

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