Evaluate each expression using the values given in the table

Evaluate each expression using the values given in the table below.

Solution

a) (f o g)(1) = f(g(1))

==> f(0) ; since g(1) = 0

==> 5

Hence (f o g)(1) = 5

b) (f o g)(2) = f(g(2))

==> f(-3) ; since g(2) = -3

==> 15

Hence (f o g)(2) = 15

c) (g o f)(2)

==> g(f(2))

==> g(1) ; since f(2) = 1

==> 0

Hence (g o f)(2) = 0

d) (g o f)(3)

==> g(f(3))

==> g(-1) ; since f(3) = -1

==> 0

Hence (g o f)(3) = 0

e) (g o g)(1)

==> g(g(1))

==> g(0)

==> 5

Hence (g o g)(1) = 5

f) (f o f)(3)

==> f(f(3))

==> f(-1)

==> 7

Hence (f o f)(3) = -7