Show that gh(-2)= 14 g(x) 2x+1/x-1 and h(x) 4x+3/x-2
Is it 2(4x+3/x-2)/x-1 and i work from there?
if g(x)=(2x+1)/(x-1)
and h(x)=(4x+3)/(x-2)
then
g(h(-2))=g(-5/-4)=g(5/4)
g(5/4)=(10/4+1)/(-1/4)=-14 if I didn't make a mistake, check me.
I will assume that by gh(-2) you mean
g(f(-2))
first do f(-2)
= -5/-4 = 5/4
now do g(5/4) = (5/2 + 1)/(5/4 - 1)
= (7/2)/(1/4)
= (7/2)(4/1)
= 14
I agree with Reiny on the +14.
To show that g(h(-2)) = 14, we need to substitute h(-2) into the expression for g(x) and simplify.
First, let's find h(-2). We substitute x = -2 into the expression for h(x):
h(x) = (4x + 3) / (x - 2)
h(-2) = (4(-2) + 3) / (-2 - 2)
= (-8 + 3) / (-4)
= -5 / -4
= 5/4
Now, let's substitute h(-2) = 5/4 into g(x) and simplify:
g(x) = 2(4x + 3) / (x - 1)
g(h(-2)) = 2(4 * (5/4) + 3) / ((5/4) - 1)
= 2(5 + 3) / (5/4 - 4/4)
= 2(8) / (1/4)
= 16 / (1/4)
= 16 * (4/1)
= 16 * 4
= 64
Therefore, g(h(-2)) = 64, not 14. So the given statement is not true.