Answer:
x=3/4
Step-by-step explanation:
Given:
f(x) = x-1
g(x) = 2x²+3
Evaluate composite functions:
f(g(x)) = f(2x²+3) = (2x²+3)-1 = 2x²+2
g(f(x)) = g(x-1) = 2(x-1)²+3 = 2(x²-2x+1)+3 = 2x²-4x+2+3 = 2x²-4x+5
Set expressions equal to each other and solve for x:
2x²+2 = 2x²-4x+5
2 = -4x+5
-3 = -4x
3/4 = x
x = 3/4
Therefore, the value of x=3/4 satisfies both composite functions
