Answer:
fg(x) = 2x² - 1
gf(x) = 4x²-12x +10
Step-by-step explanation:
Given the functions f(x) = 2x-3 and g(x) = x^2 + 1
a) f(g(x)) = f(x²+1)
f(x²+1) = 2(x²+1) -3
f(x²+1)= 2x²+2 -3
f(x²+1) = 2x² - 1
fg(x) = 2x² - 1
Hence function fg(x) is 2x² - 1
b) gf(x) = g(2x-3)
g(2x-3) = (2x-3)² + 1
g(2x-3) = (2x-3)(2x-3) + 1
g(2x-3) = 4x²-6x-6x+9 + 1
g(2x-3) = 4x²-12x +10
gf(x) = 4x²-12x +10
