Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI 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) f(x) and g(x) g(x) below, find the value of (g∘f)(−7) (g \circ f)(-7) .\newlinef(x)=2x+15g(x)=2x2+5x+4 \begin{array}{l} f(x)=2 x+15 \\ g(x)=2 x^{2}+5 x+4 \end{array} \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Transformations of quadratic functionsright chevron icon

Full solution

Q. Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of (g∘f)(−7) (g \circ f)(-7) .\newlinef(x)=2x+15g(x)=2x2+5x+4 \begin{array}{l} f(x)=2 x+15 \\ g(x)=2 x^{2}+5 x+4 \end{array} \newlineAnswer:
  1. Understand Notation: First, we need to understand the notation (g@f)(x)(g@f)(x). This notation means that we first apply the function ff to xx, and then apply the function gg to the result of f(x)f(x). This is also known as the composition of functions, denoted by (g∘f)(x)(g \circ f)(x).
  2. Find f(−7)f(-7): Now, let's find f(−7)f(-7) using the definition of f(x)=2x+15f(x) = 2x + 15.f(−7)=2(−7)+15=−14+15=1f(-7) = 2(-7) + 15 = -14 + 15 = 1.
  3. Find g(f(−7))g(f(-7)): Next, we will use the result of f(−7)f(-7) to find g(f(−7))g(f(-7)) by substituting 11 into g(x)g(x), where g(x)=2x2+5x+4g(x) = 2x^2 + 5x + 4.g(1)=2(1)2+5(1)+4=2+5+4=11g(1) = 2(1)^2 + 5(1) + 4 = 2 + 5 + 4 = 11.
  4. Conclude Result: Since we have found g(1)g(1), and we know that f(−7)=1f(-7) = 1, we can conclude that (g@f)(−7)(g@f)(-7) is equal to g(f(−7))g(f(-7)) which is g(1)g(1). Therefore, (g@f)(−7)=11(g@f)(-7) = 11.

More problems from Transformations of quadratic functions

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 1 month ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

View all (75)