Answer: options A) x = -1 and C) x = 1
Explanation:
The graph show that the two functions intersect at x = - 1 and x = 1, so those are the solutions to the equality given. That is the options A) and C).
Note that the first function, [tex]f(x)=- \frac{3}{4} x+2 \frac{1}{4} = - \frac{3}{4} x+ \frac{9}{4} [/tex] is the the straight line.
The function g(x) is [tex]( \frac{1}{2}) ^x+1[/tex]
When you replace the value of x = -1 you get:
f(-1) = - (3/4) (-1) + 9/4 = 3/4 + 9/4 = 12 / 4 = 3
g(-1) = (1/2)^(-1) + 1 = 2 + 1 = 3
So, f(-1) = g(-1).
When you replace x = 1 you get:
f(1) = -(3/4)(1) + 9/4 = -3/4 + 9/4 = 6/4 = 3/2
g(1) = (1/2)^1 + 1 = 1/2 + 1 = 3/2
So, f(1) = g(1).
And in that way you have shown analiticaly that x = -1 and x = 1 are both solutions of f(x) = g(x).
