Question

can someone help me on my college algebra homework i would really appreciate it thanks:)

1.find the default or implied domain for the following function f(x)=(x+4)/(square root (x^2=5x+6))

2.define the formula and domain for h=f+g, given the formula: f(x)=square root(4-x^2) and g(x)=square root x+1

3.define the functions h1=fg and h2= g of f, given the functions: F= (2,5) (3,4) (4,1) (5,0) and g= (1,3) (2,4) (3,1) (4,0)

4. define the composition h= g of f (find both domain and formula and simplify the formula) given the functions: f(x)=square root(2x-7) and g(x)=3x^4-2x^2

Answer 1

For number 1 is the equal a plus?

Answer 2

oh yes im sorry

Answer 3

second one
domain of
\[\sqrt{4-x^2}+\sqrt{x+1}\] you need both
\[4-x^2\geq0\] and
\[x+1\geq 0\] second inequality says
\[x\geq -1\] first one means
\[-2\leq x \leq 2\]and we combine them to see that the domain is
\[-1\leq x\leq 2\]

Answer 4

For the first one the domain includes all reals except the reals between -2 and -3. -2 and -3 are not included in the domain.

Answer 5

third one
\[f= (2,5) (3,4) (4,1) (5,0) \text{ and }g= (1,3) (2,4) (3,1) (4,0)\]
ordered pairs for
\[f\circ g\] first we do g, then we do f of the result.
g sends 1 to 3, and f sends 3 to 4, so ordered pair is (1,4)
g sends 2 to 4 and f sends 4 to 1 so ordered pair is (2,1)
g sends 3 to 1 and f sends 1 nowhere, so that is not in the domain
g sends 4 to 0 and f sends 0 nowhere, so that is not in the domain either. hence
\[f\circ g=\{(1,4),(2,1)\}\]

Answer 6

you're on your own with
\[g\circ f\] but it works similarly