Answer:
The solutions to [tex]-\frac{3}{4}x+2=(\frac{1}{4})^x+1[/tex] are (0,2) and (1,1.25).
Step-by-step explanation:
Given : The functions [tex]f(x)=-\frac{3}{4}x+2[/tex] and [tex]g(x)=(\frac{1}{4})^x+1[/tex] are shown in the graphs.
To find : What are the solutions to [tex]-\frac{3}{4}x+2=(\frac{1}{4})^x+1[/tex]?
Solution :
Expression [tex]-\frac{3}{4}x+2=(\frac{1}{4})^x+1[/tex] 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 [tex]-\frac{3}{4}x+2=(\frac{1}{4})^x+1[/tex] are (0,2) and (1,1.25).
