The function f(x) = (x − 4)(x − 2) is shown. what is the range of the function? all real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all real numbers greater than or equal to −1

All real numbers greater than or equal to -1

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex of the parabola

if  > the parabola open upward ( vertex is a minimum)

if  > the parabola open downward ( vertex is a maximum)

In this problem we have

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

> equation in vertex form

The vertex is the point

therefore

> the parabola open upward ( vertex is a minimum)

The range of the function is the interval> [-1,∞)

All real numbers greater than or equal to

-1

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.