Question

Based on the graph below, what is the solution of the equation f(x) = g(x)? graph of function f of x equals negative x plus 0.5 and graph of function g of x equals x squared plus 3 multiplied by x minus 4

Answer 1

We have that
f(x)=-x+0.5
g(x)=x²+3x-4
f(x)=g(x)------------> -x+0.5=x²+3x-4-------------> x²+3x-4+x-0.5=0

x²+3x-4+x-0.5=0---------------> x²+4x-4.5=0

using a graph tool

see the attached figure

the solution are the points (-4.915,0) and (0.915,0)