Q's

[Hye]

Hey

1.If f: R→R, where f(x)= 3− x and g:R→R, where g(x) = x^2 − 1, show that f ° g is not defined.
By restricting the domain of g, find a function h such that f ° h is defined.

[Hye]

Show that g(x) = x^4 satisfies the equation g(xy) = g(x)g(y). Show that this equation is true
for all functions of the form g(x) = x^n, where n is a natural number.

How would you "Show that this equation is true
for all functions of the form g(x) = x^n, where n is a natural number."

[the.watchman]

(1) You want for the composite to be defined

Because AND

Therefore is defined

I'm not sure, have I made a mistake?



(2)

[Hye]

The answer for 1. says R\(-1,1). Restricting the domain..

Thanks

[the.watchman]

Ok ... maybe the question is a typo, because the domain of f is R, any 'inside' graph can work

[Hye]

Question attached

thanks

[the.watchman]

Well the diagram shows that there is a turning point on the x-axis at B, which is (4,0)

Therefore, using the factorised form for the cubic equation, the graph would be , where b is the remaining intercept.

Now we can see that this graph passes through (0,3) at point G and also this point has zero gradient

So

(1)

AND because

So

(2)

Solve (1) and (2) simultaneously to get values for a and b

[vexx]

A question of similar topic

Let g:R→R,loge g(x)=ax+b. Given that g(0)=1 and g(1)=e6, find a and b and hence g(x).

[the.watchman]

I think you missed the





So ,     

,     

SO

Careful buddy

[brightsky]

 ...didn't see that.   

[the.watchman]

...didn't see that.   

Lol, good stuff anyway

[vexx]

^ your amazing, thanks:)

[the.watchman]

^ your amazing, thanks:)

No problems

[Hye]

Thanks guys

3a is y=-3/4a^2 + 3

Q3B ?

[m@tty]

For b you have to show that the corners of the barge are higher than that of the arch at that point.

You have to show that at x=1.5, -1.5  y<1.7.