1) Find the graph of a line passing through (-1, 4) and (2, 0).
The slope of two points can be determined by dividing the difference of y-values by the difference of x-values:

The slope of this equation is -4/3. Inputting this into the slope-intercept form of an equation, we get:

To find b, substitute x and y for one of the given coordinate pairs:
0 = (-4/3)(2) + b
0 = -8/3 + b
8/3 = b
Substitute the b value into the equation to finish the line:

Answer:
Step-by-step explanation:




As the equation in point-slope form

Here:
-
is a point on the line
using
and
then









Thus

comparing the equation with the slope-intercept form

so,


Therefore,
F(x)= 2/(x+1) and g(x)= -x2-12 => f(-7)= ? , g(2.5)= ?, g(f(- 0.5))= ?
In the expression of the function f(x) we will replace instead of x the number in bracket (-7) => f(-7) = 2/(-7+1)= 2/-6 = - 1/3
In the expression of the function g(x) we will replace instead of x number in bracket (2.5) => g(2.5) = - (2.5)squared -12= - 6.25 -12= - 18.25
Expression f(g(x)) or g(f(x)) is multiplication (composition) of the reflecting of functions f and g. We will do this in the following way => g(f(x))= g(2/(x+1))= -(2/(x+1))2 - 12= -(4/(x+1)2) -12= -4-12(x+1)2/(x+1)2=> we will replace instead of x the number in bracket (-0.5) or (-1/2) => g(f(-1/2) = -4-12((-1/2)+1)2/ ((-1/2+ 1)2= -4-12(1/2)2/(1/2)2=-4-12*(1/4)/(1/4)= (-4-3)/(1/4)=-28
Eaisier way => f(-1/2)=2/((-1/2)+1)=2/(1/2)= 4 g(4) -(4)2-12 = -16-12= -28
150 x .30 = 45
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Step-by-step explanation:
