f(x)=x3−5
Replace f(x)
with y
.
y=x3−5
Interchange the variables.
x=y3−5
Solve for y
.
Since y
is on the right side of the equation, switch the sides so it is on the left side of the equation.
y3−5=x
Add 5
to both sides of the equation.
y3=5+x
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
y=3√5+x
Solve for y
and replace with f−1(x)
.
Replace the y
with f−1(x)
to show the final answer.
f−1(x)=3√5+x
Set up the composite result function.
f(g(x))
Evaluate f(g(x))
by substituting in the value of g into f
.
(3√5+x)3−5
Simplify each term.
Remove parentheses around 3√5+x
.
f(3√5+x)=3√5+x3−5
Rewrite 3√5+x3
as 5+x
.
f(3√5+x)=5+x−5
Simplify by subtracting numbers.
.
Subtract 5
from 5
.
f(3√5+x)=x+0
Add x
and 0
.
f(3√5+x)=x
Since f(g(x))=x
, f−1(x)=3√5+x is the inverse of f(x)=x3−5
.
f−1(x)=3√5+x
Answer:
They would be 44.6 miles apart
Step-by-step explanation:
Here, we want to calculate how far they will be in 1 hour
Mathematically;
Distance = speed * time
In 1 hour, Kiran would have traveled a distance of 3 * 1 = 3 miles
While Clare would have traveled a distance of 3.4 * 1 = 3.4 miles
Now, we want to calculate how far apart they would be
On the 24 miles trail, Kiran would be at a distance of 21 miles to the other end
On the 24 miles Claire would be at a distance of 20.6 miles
So how far apart they would be is
24 miles + 20.6 miles = 44.6 miles
Answer:
Step-by-step explanation:
Given
Required
Find Y
To do this, we make use of the mid-point formula
i.e.
WX and ZY are the diagonals of the parallelogram.
The mid-point of WX is:
The mid-point of ZY is:
Equate both values of M
Multiply both sides by 2
By comparison:
Hence:
