Question

For the real-valued functions g(x)=x+2/x-5 and h(x)=2x+7, find the composition G o H?

Answer 1

and specify its domain using interval notation

Answer 2

What part of the problem are you getting stuck on?

Answer 3

g(h(x))=g(2x+7)
=(2x+7)+(2/((2x+7)-5))

Answer 4

so i got in the end

Answer 5

(4x^2+8x-19)/(2x+7)

Answer 6

domain is all x except x= -7/2 is this all right and how do i turn this into interval notation

Answer 7

For the domain you do NOT want

1. zero in the denominator
2. natural log of a negative number or zero
3. sqrt of a complex number

Look at g(h(x)) or to say it another way
" g of h of x" or to say it another way
g 0 h

Do you see any of these things( 1, 2 or 3 ) ?

Answer 8

no

Answer 9

so i got the right answer?

Answer 10

no wait

Answer 11

its (2x + 9)/(2x + 2)

Answer 12

g(x)=x+2/x-5 and
h(x)=2x+7

So \[\huge g(h(x)) = \frac{(2x+7) + 2}{(2x+7)-5}\]
which is equal to

\[\huge g(h(x)) = \frac{2x+9}{2x+2}\]

Answer 13

yes

Answer 14

Ok, it is taking me too long to type in the LaTeX. ;-p

Answer 15

The denominator cannot equal zero.

So when is 2x + 2 = 0 ?

Answer 16

its domain is all x such that 2x + 2 ≠ 0 --> x ≠ - 1

Answer 17

Yes.
In interval notation you would write something like... \[\huge (-\infty, -1)\cup (-1, \infty)\]

But it's much easier to just write \[x \neq 0\] :-p

Answer 18

kk thanks

Answer 19

No prob.