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
X²-5x-36
Write -5x as a sum or difference.
x²+4x-9x-36
Factor out x from the expression.
x(x+4)-9(x+4)
Factor out x+4 from the expression.
(x+4)(x-9)
Answer: The second step is to factor out x.
Answer:
<em>She needs </em><em>77 </em><em>on her last test to earn an 82 for the quarter.</em>
Step-by-step explanation:
Maria scored 72, 97, and 82 on her first three math tests.
She wants to have a mean score of 82 for the quarter.
Let us assume that she must score x on her last test to earn an 82 for the quarter.
So the average score will be,
But the average score is given as 82, so
11^2=121
12^2=144
You can write either 11 or 12.
The formula for the volume of a cone is V= πr² (h/3).
V= 3.14 (12²) (8/3)
V= 3.14 (144) (2.6...)
V= 1205.76
V≈ 1206
So the answer is A.
