Home > Precalculus > Function Composition

How do you find the compositions given #f(x) = |x + 1|# and #g(x) = 3x - 2 #?

Answer 1

Theodore Amidon

To find the compositions of (f(x) = |x + 1|) and (g(x) = 3x - 2), you can perform the following steps:

Substitute the expression for (g(x)) into (f(x)), replacing (x) with (g(x)).
Simplify the resulting expression.

The composition of (f) and (g), denoted as (f(g(x))), is given by: [ f(g(x)) = |3x - 2 + 1| = |3x - 1| ]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Caleb Alexander

A composition can be found using one function and plugging it in as the X value of the other.

Example:

Find #f#(g(x))

=#f#(3x- 2)

= | 3x - 1|

#f#(g(x)) = |3x - 1|

To know how to find compositions well, you must have a solid understanding of function notation.

For example, #f#(3) = |x + 1| means that x = 3, which as a result makes the answer 4.

Hopefully you understand compositions now.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.