Answer:
The decimal 3.75 would be 3 75/100 as a mixed number.
Step-by-step explanation:
75/100 expressed in the simplest fraction is 3/4.
Case a)
f(x)=[x-1]/[x+5]
step 1
f(x)=y
y=[x-1]/[x+5]
step 2
exchange x for y and y for x
y=[x-1]/[x+5]------> x=[y-1]/[y+5]----> x*[y+5]=[y-1]----> xy+5x=y-1
step 3
clear the variable y
xy+5x=y-1-----> y-xy=5x+1----> y*[1-x]=[5x+1]----> y=[5x+1]/[1-x]
step 4
f(x)-1= [5x+1]/[1-x]
the function and the inverse function are not the same
case b)
g(x)=[x-2]/[x-1]
step 1
g(x)=y
y=[x-2]/[x-1]
step 2
exchange x for y and y for x
y=[x-2]/[x-1]------> x=[y-2]/[y-1]----> x*[y-1]=[y-2]----> xy-x=y-2
step 3
clear the variable y
xy-x=y-2-----> xy-y=-2+x----> y*[x-1]=[x-2]----> y=[x-2]/[x-1]
step 4
g(x)-1= [x-2]/[x-1]
the function and the inverse function are the same
case c)
h(x)=[x+3]/[x-2]
step 1
h(x)=y
y=[x+3]/[x-2]
step 2
exchange x for y and y for x
y=[x+3]/[x-2]------> x=[y+3]/[y-2]----> x*[y-2]=[y+3]----> xy-2x=y+3
step 3
clear the variable y
xy-2x=y+3-----> xy-y=3+2x----> y*[x-1]=[2x+3]----> y=[2x+3]/[x-1]
step 4
h(x)-1= [2x+3]/[x-1]
the function and the inverse function are not the same
case d)
k(x)=[x+1]/[x-1]
step 1
k(x)=y
y=[x+1]/[x-1]
step 2
exchange x for y and y for x
y=[x+1]/[x-1]------> x=[y+1]/[y-1]---> x*[y-1]=[y+1]----> xy-x=y+1
step 3
clear the variable y
xy-x=y+1-----> xy-y=x+1----> y*[x-1]=[x+1]----> y=[x+1]/[x-1]
step 4
k(x)-1= [x+1]/[x-1]
the function and the inverse function are the same
Answer:
x=
Step-by-step explanation:
3x-12-6x+21=23
-3x+9=23
-3x=14
x=
Answer:
After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46
Step-by-step explanation:
We need to complete the square:
x^2 − 4x − 8 = 0
x^2 -2(x)(2)+(2)^2 -8 -4 =0
(x^2 -4x +4) - 12 = 0
(x-2)^2 -12 =0
Now, finding the value of x
(x-2)^2 -12 =0
(x-2)^2 = 12
taking square root on both sides
So, After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46
Answer:
Domain: (
−
∞
,
∞
)
, {
x
|
x
∈
R}
Range: (
−
∞
,
∞
)
, {
y
|
y
∈
R}
Step-by-step explanation:
We can simplify to understand how to answer the question better.
<em>5 * 11x = 55x</em>
<u>Function range definition:</u><u> </u>
The set of values of the dependent variable for which a function is defined.
- The range of polynomials with odd degree is all real numbers.
<u>So the solution is.. </u>
-∞<x<
∞
<u>And the interval notation is..</u>
(-
∞.
∞)
