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 =)
we want $\displaystyle 3(x^2 + 2x - 3) + 5 = (3x + 5)^2 + 2(3x + 5) - 3$
now solve for x
i suppose they want us to do this the hard way. so first thing's first. find $\displaystyle f^{-1}(x)$ and then we'll take it from there.2)If f(x)=2x-7 and g(x)=5-2x,
a)determine fof^-1 and f^-1of.
find $\displaystyle (f \circ g)(x)$ and then it's inverseb)show that (fog)^-1=g^-1of^-1
thank you =)
then find $\displaystyle g^{-1}(x)$ (you already found $\displaystyle f^{-1}(x)$
then just show that both expressions are equal. that is, find and simplify $\displaystyle (f \circ g)^{-1}(x)$ and show that you get the same expression as when you find and simplify $\displaystyle (f^{-1} \circ g^{-1})(x)$
for the first question i got...
3$\displaystyle x^2$+6x-9+5=(3x+5)$\displaystyle ^2$+2(3x+5)-3
3$\displaystyle x^2$+6x-4=9$\displaystyle x^2$+15x+15x+25+6x+7
3$\displaystyle x^2$+6x-4=9$\displaystyle x^2$+36x+32
is this answer close to the final answer?