Question

For all values of x, f(x)=x-1 and g(x)=2x^2+3. Solve fg(x)=gf(x)

Answer 1

x=3/4

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