Answer:
There does not exist any solution of [tex]f(x)=g(x)[/tex] as thir graphs do not intersect.
Step-by-step explanation:
We are given that,
The values of the exponential function f(x) are f(1)= 2 and f(2)= 6.
That is, we get,
[tex]f(1)=2=2\times 3^0[/tex]
[tex]f(2)=2=2\times 3^1[/tex]
So, the function f(x) is [tex]f(x)=2(3)^x[/tex].
Moreover, the values of the linear function g(x) are g(1) = 2.5 and g(2) = 4.
That is, the slope = [tex]\frac{4-2.5}{2-1}[/tex] = 1.5
Substituting the slope and point (1,2.5) in the linear equation [tex]y=mx+b[/tex], where m is the slope, we get,
[tex]2.5=1.5\times 1+b[/tex]
i.e. b= 1
Thus, the function g(x) is [tex]g(x)=2.5x+1[/tex].
Consider, [tex]f(x)=g(x)[/tex]
i.e. [tex]2(3)^x=2.5x+1[/tex]
Now, the function f(x) is exponentially increasing and the linear function g(x) is increasing between x= 1 and x= 2, but there is no point where the graphs of the functions are intersecting.
Thus, there is no solution of the equation [tex]f(x)=g(x)[/tex].
