Mastering Composite Functions: Examples, Problems, and Solutions

For the given functions f and g, find:
(a) $f \circ g$
(b) $g \circ f$
(c) $f \circ f$
(d) $g \circ g$
State the domain of each composite function.
$f (x) = \frac{1}{x + 3} . g (x) = - \frac{2}{x}$

avissidep 2021-09-12

Given $f (x) = 4 x^{2} - 3 and g (x) = 6 - \frac{1}{2} x^{2}$
a. (f of g)(4)

defazajx 2021-09-09

Given $f (x) = 4 x^{2} - 3 and g (x) = 6 - \frac{1}{2} x^{2}$
b. $(g o f f) (2)$

tricotasu 2021-09-09

In plainspeak, what do composite functions do?

Marvin Mccormick 2021-09-07

Given $f (x) = 4 x^{2} - 3 and g (x) = 6 - \frac{1}{2} x^{2}$
c. $(f o f f) (1)$

Anonym 2021-09-06

Evaluate the function at given value of the independent variable. Simplify the results.
$f (x) = \sqrt{x + 5}$
$f (- 4)$

SchachtN 2021-09-06

I must have made a mistake in finding the composite functions $f \circ g and g \circ f,$ because I notice that $f \circ g$ is not the same function as $g \circ f$ .Determine whether the statement makes sense or does not make sense, and explain your reasoning.

ossidianaZ 2021-09-03

Evaluate the function at given value of the independent variable. Simplify the results.
$f (x) = \sqrt{x + 5}$
$f (4)$

Emeli Hagan 2021-09-02

Find composite function $f \circ g and g \circ f$ . Find the domain of each composite function. Are the two composite funcctions equal?
$f (x) = x^{2}$
$g (x) = \sqrt{x}$

sibuzwaW 2021-06-28

Find derivatives of the functions defined as follows.
$y = 4^{- 5 x + 2}$

Albarellak 2021-06-24

Find derivatives of the functions defined as follows.
$y = 3 \dot{{} 4^{x^{2} + 2}$

Nannie Mack 2021-06-21

Find derivatives of the functions defined as follows.
$f (z) = {(2 z + e^{- z^{2}})}^{2}$

ka1leE 2021-06-13

Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as $(x, y) \to (0, 0) . f (x, y) = 1 - \frac{\cos (x^{2} + y^{2})}{x^{2} + y^{2}}$

lwfrgin 2021-06-11

Write an integral that requires three applications of integration by parts. Explain why three applications are needed.

Kye 2021-05-30

Find the limit and discuss the continuity of the function. $lim (x, y, z) \to (- 2, 1, 0) x e^{y} z$

midtlinjeg 2021-05-28

Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as $(x, y) \to (0, 0) . f (x, y) = e^{x y}$

DofotheroU 2021-05-19

Use limit laws and continuity properties to evaluate the limit.
$lim_{(x, y) \to (4, - 2)} x \sqrt{3} {y^{3} + 2 x}$

Amari Flowers 2021-05-16

Sketch the graph of the function
a) $f (1) = [[1]] + [[- 1]] = 1 \pm 1 = 0$

$f (0) = 0$

$f (\frac{1}{2}) = 0 \pm 1 = - 1$

$f (- 2.7) = - 3 + 2 = - 1$

b) $lim_{x \to 1} f (x) = - 1$

$lim_{x \to 1 +} f (x) = - 1$

$lim_{x \to \frac{1}{2}} f (x) = - 1$

c) f is continuous for all real numbers except $0, \pm 1, \pm 2, \pm 3, \pm 4 \dots$

Josalynn 2021-05-16

Find derivatives of the functions defined as follows.
$p = \frac{1000}{9 + 4 e^{- 0.2 t}}$

Nann 2021-05-02

Find the limit and discuss the continuity of the function. $lim (x, y) \to (0, 0) x + 4 y + 1$

The composite functions examples and solutions are vital for the correct understanding of this aspect of Precalculus. Dealing with Composite Functions for your Engineering task will seem much easier as you look through the list of helpful questions and answers.

If something that you need looks similar to what we have included below, start with the analysis of composite aspect by exploring our examples. It will help you receive the best kind of help because the solutions below have the best examples and use of integral calculus in real life.

Precalculus

Practice Exercises for Composite Functions