Calculating g(f(5)) for Composite Functions

[ghostbuster25]

Im looking for g(f(5))

where f(x) = X^2 - 3x

and g(x) = 8 + 2x - x^2 xER and x is greater than or equal to 1

I have first found f(5)
(5)^2-3(5)
which equals 10

However when i do g(10)
8+2(10)-(10)^2

that gives me a negative number of -72! Which can't be right because g has to greater than or equal to 1

Where am i going wrong?

 

[cyby]

No. What you said was that x has to be $\geq 1$, not g. There is a difference - can you tell me what the difference is?

 

[ghostbuster25]

No. What you said was that x has to be $\geq 1$, not g. There is a difference - can you tell me what the difference is?

is it because g is a gunction of x, not x itself!? am i doing it correctly then? :)

 

[cyby]

The difference is that you're limiting the *domain* of g to be positive. This said nothing about the function must evaluate to.

What this is essentially saying is that g(1) is ok, but g(0.5) isn't, because 0.5 is < 1.

Everything else looks good.

 

[ghostbuster25]

ahhh yer that makes sense :) thanks