let f(x)=x^2-2x and g(t)=2t+5

Question

1.      Let

f (x) = x^2 - 2x and g (t ) = 2t + 5 .

a.) If x = 4 , find f (4) . Now find g ( f (4)). This is called composing g with f.

b.) If we let h (x) = g ( f (x)), find an explicit algebraic formula for h.

c.) Now find a formula for f (g (t )) .

d.) Is g ( f (x)) = f (g (t ))? Why or why not?

Answer 1

a) f(4) = 16-8 = 8, g(f(4) = g(8) = 16+5 =21 if x=t

b) g(f(x)) = 2(x^2-2x)+5 = 2x^2-4x+5 = h(x)

c) f(g(t) = f(2t+5) = (2t+5)^2 -2(2t+5) = 4t^2 + 20t + 25 -4t -10 = 4t^2+16t +15 which doesn't equal g(f(x) even if t=x

d) f and g are not inverses. f(g) = g(f) only if the two functions are inverses of each other