Composition of Functions Examples 2

In this class, We discuss the Composition of Functions Examples 2.

The reader should have prior knowledge of the composition of functions. Click Here.

Example 1:

f: R -> R f(x) = x^2 – 2

g: R -> R g(x) = x + 4

Find fog and gof?

1) fog(x) = f(g(x))

f(x + 4)

(x + 4)^2 -2

x^2 +18x +14

2) gof(x) g(f(x))

g(x^2 – 2)

x^2 -2 + 4

x^2 + 2

Example 2:

f(x) = x+2

g(x) = x – 2

h(x) = 3x

Find fohog?

(fohog)(x) = f(h(g(x)))

f(h(x-2))

f(3x -6)

3x – 6 + 2

3x – 4

Example 3:

f: R -> R f(x) = -x^2

g: R+ -> R+ g(x) = sqrt(x)

Find fog?

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

f(sqrt(x))

= -x

g(x) works on R+

fog: R+ -> R = -x

gof is not possible