functions of x

Question

far all values of x, f(x)=x²+1    g(x)=x-5

 

a) show that fg(x) = x²–10x+26

 

b) solve fg(x) = gf(x)

Answer 1

f(x) = x² + 1

g(x) = x - 5

 

f(g(x)) = g(x)² + 1 = (x-5)² + 1

Can you finish it from here?

 

f(g(x)) = x2 - 10x + 26

g(f(x)) = f(x) - 5 = x² + 1 - 5 = x² - 4

 

f(g(x)) = f(g(x))

x² - 10x + 26 = x² - 4

Solve for x.