Thread: composite functions :o

1)If f(x)=3x+5 and g(x)=x^2+2x-3, determine x such that f(g(x))=g(f(x)).

2)If f(x)=2x-7 and g(x)=5-2x,
a)determine fof^-1 and f^-1of.
b)show that (fog)^-1=g^-1of^-1

thank you =)

Originally Posted by johett

1)If f(x)=3x+5 and g(x)=x^2+2x-3, determine x such that f(g(x))=g(f(x)).

we want

now solve for x

2)If f(x)=2x-7 and g(x)=5-2x,
a)determine fof^-1 and f^-1of.

i suppose they want us to do this the hard way. so first thing's first. find and then we'll take it from there.

b)show that (fog)^-1=g^-1of^-1

thank you =)

find and then it's inverse

then find (you already found

then just show that both expressions are equal. that is, find and simplify and show that you get the same expression as when you find and simplify

for the first question i got...

3 +6x-9+5=(3x+5) +2(3x+5)-3
3 +6x-4=9 +15x+15x+25+6x+7
3 +6x-4=9 +36x+32
is this answer close to the final answer?

Originally Posted by johett

for the first question i got...

3 +6x-9+5=(3x+5) +2(3x+5)-3
3 +6x-4=9 +15x+15x+25+6x+7
3 +6x-4=9 +36x+32
is this answer close to the final answer?

why don't you finish?

by the way, it's ok to type the whole line between the math tags. it looks weird when you just put the x-squared in there

doesn't look better?