Creating Functions through Composition

Solving linear equations

Defining function composition expressions

Graphing functions

Evaluating functions at a point

The output of f(x)

The input to f(x)

A constant value

An independent variable

x^2

g(x)

1 + x

f(x)

1 / (x + 1)

sqrt((x / (1 + x))^2 - 1)

sqrt(x^2 - 1)

x^2 / (1 + x^2)

sqrt(x^2 - 1)

1 / (x + 1)

x^2 / (1 + x^2)

sqrt((x / (1 + x))^2 - 1)

An independent variable

A constant value

The input to g(x)

The output of g(x)

1 + x

x^2

g(x)

f(x)

sqrt(x^2 - 1)

sqrt((x / (1 + x))^2 - 1)

sqrt(x^2 - 1) / (1 + sqrt(x^2 - 1))

1 / (x + 1)

No, unless the functions are linear

Yes, they are always the same

No, they are generally different

Yes, if x is a constant

1 / (x + 1)

sqrt((x / (1 + x))^2 - 1)

sqrt(x^2 - 1)

sqrt(x^2 - 1) / (1 + sqrt(x^2 - 1))