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1.) Sqrt /2x+6/-4=0
Isolate sqrt /2x+6/=4+0
sqrt /2x+6/=4
square both sides
sqrt /2x+6/^2=4^2
2x+6=16
solve
2x+6-6=16-6
2x=10
2x/2=10/2
x=5
2.) 3(x-6)^3/4=81
divide by 3
(x-2)^3/4=27
raise it to the reciprocal
x-2=27^4/3
add two
x-2+2=27^4/3+2
x=29^4/3
3.) V=8500^3
8500=pi/6 x d^3
4.)x= sqrt/2x-12/+6
isolate
-sqrt/2x-12/=-x+6
sqrt/2x-12/=x-6
square both sides
sqrt/2x-12/^2=x-6^2
2x-12=x^2-12x+36
rearrange it to a quadratic equation
x^2 - 14x + 48 = 0
solve
14+-sqrt-14)^2-4(1)(48)/2(1)
14+-sqrt 4/2
14+- 2 sqrt 1/ 2
7+- 1 sqrt 1 = 8,6
x=(8,6)
5.) sqrt 4y+4 - sqrt 3y+9
Square both sides
sqrt 4y+4^2 - sqrt 3y+9^2
4y+4 - 3y+9
y-5+5=0+5
y=5
6.) f(x) =3x^2+6 g(x)=4x^2
distribute
(f+6)(x)
7.)
8.) f(x)=5x-1 g(x)=x^2-3
(f x g) (6)
(5x-1 x x^2-3) (6)= 6x^2-3
6=6x^2-3
36x^2-9
9.) f(x)=9.09x g(y)0.14y
f(x)=y=9.09x
g(y)=0.14y
g(9.09)=0.14y
multiply
=1.27
1.25(30)
$38.10
10.)y=5x-3
rearrange variables
x=5y-3
solve for y
5y−3=x
5y−3+3=x+3
5y=x+3
5y/5=3/5 +x/5
y=3/5+x/5
yes it is a function
11.) y=3x+2
x=3y/3+2/3
y= 1/3x-2/3
yes it is a function
graph on other attachment
red=y=1?3x+2/3
blue= y=3x+2
12.) y= sqrt x-1
sqrt x-1 =y
sqrt x-1^2 =y^2
x-1=y^2
x-1+1=y^2+1
y=x^2+1
The domain is all real numbers greater than 1
the range is all real numbers greater than 0
13.)f(x)=4x-4
(f x f^-1)(-4)=-4
14.) A.
15.) C.
16.) x= sqrt 4x-5 = 11
sqrt 4x-5^2 = 11^2
4x-5=22
4x-5+5=22+5
4x=27
x=6.75
17.) To obtain the graph of g(x)= 3 sqrt x to f(x) 3 sqrt x+3 you need to shift the graph three units up
18.)y= sqrt 36x-144^2
y=36x-144
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