Graph f(x)=2^x+1 and g(x)=−x+4 on the same coordinate plane. what is the solution to the equation f(x)=g(x) ? enter your answer in the box. x =

The solution to the equation f(x)=g(x) is (1,3)

Step-by-step explanation:

Given . We have to find the solution to the equation f(x)=g(x).

The graph of   and can be drawn.

The graph of g(x)=−x+4  is a straight line, with the same gradient throughout.

The graph of   can also be drawn using two reference points, e.g.  (0,2)  and  (1,3) .

The coordinates at which these graphs meet are   (1,3)  .

Hence, the solution to the equation f(x)=g(x) is (1,3)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is