Given the function f(x) = -2c + cx - x^2? and f^-1(5) = -1, find c.

c = - 2

Step-by-step explanation:

Given inverse function

(5) = - 1 , then

f(- 1) = 5 , that is

- 2c + c(- 1) - (- 1)² = 5

- 2c - c - 1 = 5

- 3c - 1 = 5 ( add 1 to both sides )

- 3c = 6 ( divide both sides by - 3 )

c = - 2

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have