can someone help me with this question quickly I need it by tomorrow is really confusing please......I'm desperate
1.a function is given as f(x)=9x^2+3x.
A.if f(x)=(g·h)(x), state two possible pairs of equation for g(x)and h(x).
B. if f(x)=(g o f)(x),state two possible pairs of equation for g(x) and h(x)
2.if f={(1,4),(2,7),(3,1)}, determine (f o f)(3) and explain.
thank you for your help...
3 years ago
Answered By Michael Z
So with these types of questions you can be a bit creative:
a) you just need to make up two functions g(x) and h(x) where if you multiply them you get the function f(x)=9x2+3x, so one of the solutions could be g(x)= 3x and h(x)=3x+3 and this is obtained by factoring f(x)
b) I'm assuming you mean f(x)=(goh)(x). This is a composite function and we are looking for a function h(x) which we substitute into g(x) to produce our f(x)=9x2+3x. So h(x)=x2 and $g\left(x\right)=9x+3\sqrt{x}$g(x)=9x+3√x. Another solution is that we can say h(x)= 3x and g(x)=x2+x.
2. So if f(3)= 1 then fof (3) means that I take first f(3) and substitute it into f(x) again. It looks like this f(f(3))=f(1)=4
3 years ago
Answered By Michael Z
sorry just to edit a mistake for a) h(x)= 3x+1