SOLUTION: Need help once again, can't seem to figure this out. Let h and g be two functions defined by h(x)=(5+x)(-6+x) g(x)=2-x for any real number x. Find h/g(3) and then find al

Question 528003: Need help once again, can't seem to figure this out.
Let h and g be two functions defined by
h(x)=(5+x)(-6+x)
g(x)=2-x
for any real number x.
Find h/g(3) and then find all values that are NOT in the domain of h/g. If there is more than one value, separate them with commas.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
h(x)=(5+x)(-6+x)

h(3)=(5+3)(-6+3)

h(3)=(8)(-3)

h(3) = -24
----------

g(x)=2-x

g(3)=2-3

g(3) = -1

-----------------------------

(h/g)(x) = (h(x))/(g(x))

(h/g)(3) = (h(3))/(g(3))

(h/g)(3) = -24/(-1)

(h/g)(3) = 24

======================================

Since you CANNOT divide by zero, this means that the denominator g(x) cannot be zero.

If it were, then g(x) = 0 would mean that 2-x = 0 and that x = 2

So x = 2 makes the denominator zero. So we must exclude that from the domain.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

RELATED QUESTIONS
let g and h be two functions defined by: g(x)=(x-1)(x-6) h(x)=-9x+1 for any... (answered by josgarithmetic)

Let h and g be two functions defined by h(x)=(x-3)(x+5) g(x)=-2x+1 for any real... (answered by MathLover1)

Let g and h be two functions defined by: g(x)= x+4 h(x)= x^2+18x+81 for any real... (answered by robertb)

Let g and h be two functions defined by g(x)=x-8 h(x)=(x-5)(x-4) For any realnumber... (answered by Theo)

g(x) = x²+mx+b h(x) = g(x-2) Two quadratic functions g and h are defined by the... (answered by ikleyn)

If the functions g, h are defined by g(x) = x - 3, h(x) = 4x^2, write a formula for the... (answered by ewatrrr)

can not figure this out Find functions f and g so that (fog)= H(x) and H(x)=√x^2 (answered by ewatrrr)

Suppose H(x)=√6x-1. Find two functions f and g such that (f °g)(x) = H(x)... (answered by greenestamps)

Suppose that the functions g and h are defined for all real numbers x as follows.... (answered by solver91311)