Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Given the definitions of f(x) and g(x) below, find the value of (g@f)(-7). {:[f(x)=2x+15],[g(x)=2x^(2)+5x+4]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $(g \circ f)(-7)$ . $\newline$ $\begin{array}{l} f(x)=2 x+15 \\ g(x)=2 x^{2}+5 x+4 \end{array}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Transformations of quadratic functions

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

(g \circ f)(-7)

.

\newline

\begin{array}{l} f(x)=2 x+15 \\ g(x)=2 x^{2}+5 x+4 \end{array}

\newline

Answer:

Understand Notation: First, we need to understand the notation $(g@f)(x)$ . This notation means that we first apply the function $f$ to $x$ , and then apply the function $g$ to the result of $f(x)$ . This is also known as the composition of functions, denoted by $(g \circ f)(x)$ .
Find $f(-7)$ : Now, let's find $f(-7)$ using the definition of $f(x) = 2x + 15$ . $f(-7) = 2(-7) + 15 = -14 + 15 = 1$ .
Find $g(f(-7))$ : Next, we will use the result of $f(-7)$ to find $g(f(-7))$ by substituting $1$ into $g(x)$ , where $g(x) = 2x^2 + 5x + 4$ . $g(1) = 2(1)^2 + 5(1) + 4 = 2 + 5 + 4 = 11$ .
Conclude Result: Since we have found $g(1)$ , and we know that $f(-7) = 1$ , we can conclude that $(g@f)(-7)$ is equal to $g(f(-7))$ which is $g(1)$ . Therefore, $(g@f)(-7) = 11$ .

More problems from Transformations of quadratic functions

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 8 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 7 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 5 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 5 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 5 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 5 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 5 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 4 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant