Question

2.     Consider three functions f, g, and h (from R to R+). Let f (x) = x², g(x) = 2^x and h(x) = log₂(x)

a)  Evaluate f ◦ g(0)

b)  Evaluate h ◦ g(5)

c)  Evaluate h ◦ f(0)

d)  Give a mathematical expression for h ◦ g

e)  Give a mathematical expression for h ◦ g ◦ f

Answer 1

a)

$f ◦ g(x)=(2^x)^2$

$f ◦ g(0)=(2^0)^2=1$

b)

$h ◦ g(x)=log_2(2^x)=x$

$h ◦ g(5)=5$

c)

$h ◦ f(x)=log_2(x^2)$

$h ◦ f(0)=log_2(0)=-\infin$

d)

$h ◦ g=log_2(2^x)=x$

e)

$h ◦ g ◦ f=log_2(2^{x^2})=x^2$