Question

The following values represent exponential function ƒ(x) and linear function g(x). ƒ(1) = 2 g(1) = 2.5

Answer 1

The function f(x) does not have a value of x that satisfies the given solutions, while the function g(x)=1.5+1. 

Answer 2

Answer:

There does not exist any solution of $f(x)=g(x)$ 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,

$f(1)=2=2\times 3^0$

$f(2)=2=2\times 3^1$

So, the function f(x) is $f(x)=2(3)^x$.

Moreover, the values of the linear function g(x) are g(1) = 2.5  and g(2) = 4.

That is, the slope = $\frac{4-2.5}{2-1}$ = 1.5

Substituting the slope and point (1,2.5) in the linear equation $y=mx+b$, where m is the slope, we get,

$2.5=1.5\times 1+b$

i.e. b= 1

Thus, the function g(x) is $g(x)=2.5x+1$.

Consider, $f(x)=g(x)$

i.e. $2(3)^x=2.5x+1$

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 $f(x)=g(x)$.