Question

The functions f (x)=−3/4x+2 and g (x)=(1/4)ˣ+1 are shown in the graph.

What are the solutions to −3/4x+2=(1/4)ˣ+1?

Answer 1

The solutions to
`-(3)/(4)x+2=((1)/(4))^x+1` are (0,2) and (1,1.25).

Explanation:

Given : The functions
`f(x)=-(3)/(4)x+2` and
`g(x)=((1)/(4))^x+1` are shown in the graphs.

To find : What are the solutions to
`-(3)/(4)x+2=((1)/(4))^x+1`?

Solution :

Expression
`-(3)/(4)x+2=((1)/(4))^x+1` means f(x)=g(x)

We know that, If two functions are equal then there solution is the intersection point of the curves.

When we determine the graph the intersection points are (0,2) and (1,1.25).

Refer the attached figure for clearance.

Therefore, The solutions to
`-(3)/(4)x+2=((1)/(4))^x+1` are (0,2) and (1,1.25).

Answer 2

The graphs cross at x=0 and x=1. Those are the solutions to f(x) = g(x).