Answer:
Option c.
Step-by-step explanation:
Given,
f(x) = y = 3x^6
To find f^-1(x), we just need to replace y with x, and x with y
x = 3*y^6
Now we solve for y
f(x)^-1 = y = ±(x/3)^(1/6)
To quickly see if it is a function, we can plot it using an graphing calculator or any plotting tool.
Please see attached picture.
By looking at the plot, we can tell f(x)^-1 is not a function, because for a single value of x, there are two corresponding values of y
Correct answer:
Option C.
Answer:
The solution to the system is the pair (9, 6)
Step-by-step explanation:
Hi!
First, let´s write the system of equations:
-y² + 6y + x -9 = 0
6y = x +27
The solutions of the system are the pairs (x, y) that satisfy both equations.
Let´s take the second equation and solve it for x:
6y = x +27
Subtract 27 from both sides of the equation
6y - 27 = x
Now, we can replace x in the first equation and solve it for y:
-y² + 6y + x -9 = 0
-y² + 6y + 6y - 27 -9 = 0
-y² + 12y - 36 = 0
Notice that -y² + 12y - 36 = -(y - 6)², then:
-(y - 6)² = 0
y - 6 = 0
y = 6
(alternatively you can solve the quadratic equation using the quadratic formula).
Now let´s find the value of x:
x = 6y -27
x = 6·6 -27
x = 9
The solution to the system is the pair (9, 6)
Please see the attached figure. The point where the curves intersect is the solution to the system.
