Question

The function f(x) is exponential and the function g(x) is linear, These functions have the following values: f(1) = 2 g(1) - 2.5 f(2)= 6 g(2) = 4 It follows that there must be a solution to f(x) = g(x) between x = 1 and x = 2.

True
False​

Answer 1

Explanation:

There does not exist any solution of 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,

So, the function f(x) is .

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

That is, the slope = = 1.5

Substituting the slope and point (1,2.5) in the linear equation , where m is the slope, we get,

i.e. b= 1

Thus, the function g(x) is .

Consider,

i.e.

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 .