1. ## 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 =)

2. 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 $3(x^2 + 2x - 3) + 5 = (3x + 5)^2 + 2(3x + 5) - 3$

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 $f^{-1}(x)$ and then we'll take it from there.

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

thank you =)
find $(f \circ g)(x)$ and then it's inverse

then find $g^{-1}(x)$ (you already found $f^{-1}(x)$

then just show that both expressions are equal. that is, find and simplify $(f \circ g)^{-1}(x)$ and show that you get the same expression as when you find and simplify $(f^{-1} \circ g^{-1})(x)$

3. for the first question i got...

3 $x^2$+6x-9+5=(3x+5) $^2$+2(3x+5)-3
3 $x^2$+6x-4=9 $x^2$+15x+15x+25+6x+7
3 $x^2$+6x-4=9 $x^2$+36x+32

4. Originally Posted by johett
for the first question i got...

3 $x^2$+6x-9+5=(3x+5) $^2$+2(3x+5)-3
3 $x^2$+6x-4=9 $x^2$+15x+15x+25+6x+7
3 $x^2$+6x-4=9 $x^2$+36x+32
doesn't $3x^2 + 6x - 9 + 5 = (3x + 5)^2 + 2(3x + 5) - 3$ look better?