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:

The form of your answer should either be p(x)p(x) or p(x)+kx−3p(x)+\frac{k}{x-3} where p(x)p(x) is a polynomial and kk is an integer. 4x3−14x2−7x−4x−4\frac{4x^3-14x^2-7x-4}{x-4}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Composition of linear and quadratic functions: find an equationright chevron icon

Full solution

Q. The form of your answer should either be p(x)p(x) or p(x)+kx−3p(x)+\frac{k}{x-3} where p(x)p(x) is a polynomial and kk is an integer. 4x3−14x2−7x−4x−4\frac{4x^3-14x^2-7x-4}{x-4}
  1. Identify Problem Type: Identify the type of problem and the method to solve it. We need to simplify the rational expression by performing polynomial long division.
  2. Set Up Division: Set up the division of (4x3−14x2−7x−4)(4x^3 - 14x^2 - 7x - 4) by (x−4)(x - 4). Start dividing the highest degree terms: Divide 4x34x^3 by xx to get 4x24x^2.
  3. Multiply and Subtract: Multiply 4x24x^2 by (x−4)(x - 4) and subtract from the original polynomial.\newline4x2×(x−4)=4x3−16x24x^2 \times (x - 4) = 4x^3 - 16x^2\newline(4x3−14x2−7x−4)−(4x3−16x2)=2x2−7x−4(4x^3 - 14x^2 - 7x - 4) - (4x^3 - 16x^2) = 2x^2 - 7x - 4
  4. Divide New Term: Divide the new term 2x22x^2 by xx to get 2x2x. Multiply 2x2x by (x−4)(x - 4) and subtract from the current polynomial. 2x∗(x−4)=2x2−8x2x * (x - 4) = 2x^2 - 8x (2x2−7x−4)−(2x2−8x)=x−4(2x^2 - 7x - 4) - (2x^2 - 8x) = x - 4
  5. Divide xx: Divide xx by xx to get 11.\newlineMultiply 11 by (x−4)(x - 4) and subtract from the current polynomial.\newline1×(x−4)=x−41 \times (x - 4) = x - 4\newline(x−4)−(x−4)=0(x - 4) - (x - 4) = 0

More problems from Composition of linear and quadratic functions: find an equation

Question
Find the inverse of the function. y=x+3 y = x + 3 Write your answer in the form ax+b ax + b . Simplify any fractions. y= y = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find (r∘s)(x)(r \circ s)(x).\newliner(x) = 33x\newlines(x) = 22x + 55\newlineWrite your answer as a polynomial in simplest form.\newline(r∘s)(x)=(r \circ s)(x) = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
What is (f+g)(x)(f + g)(x)?\newlinef(x)=−3xf(x) = -3x\newlineg(x)=3x+1g(x) = 3x + 1\newline\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline‾\underline{\hspace{3cm}}\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x+4f(x) = -x + 4\newlineg(x)=4xg(x) = 4x\newline\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline‾\underline{\hspace{3em}}\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the domain of (fg)(x)\left(\frac{f}{g}\right)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=−5x+3g(x) = -5x + 3\newlineChoices:\newline[A]All real numbers[\text{A]All real numbers}\newline[B]All real numbers except 35[\text{B]All real numbers except } \frac{3}{5}\newline[C]All real numbers except −35[\text{C]All real numbers except } -\frac{3}{5}\newline[D]All real numbers except 53[\text{D]All real numbers except } \frac{5}{3}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the inverse of the function.\newliney = −3x-3x \newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find (f∘g)(0)(f \circ g)(0).\newlinef(x)=6xf(x) = 6x\newlineg(x)=x2+4xg(x) = x^2 + 4x\newline(f∘g)(0)=(f \circ g)(0) = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find (f∘g)(x)(f \circ g)(x).\newlinef(x)=x2+5f(x) = x^2 + 5\newlineg(x)=4xg(x) = 4x\newlineWrite your answer as a polynomial in simplest form.\newline(f∘g)(x)=(f \circ g)(x) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Is f(x) f(x) the inverse function of g(x) g(x) ?\newlinef(x)=x f(x) = x \newlineg(x)=−4x g(x) = -4x \newlineChoices:\newline[yes] \text{[yes]} \newline[no] \text{[no]}
Get tutor helpright-arrow

Posted 1 month ago

Question
What is (f∗g)(x)(f * g)(x)? f(x)=3x2+9xf(x) = 3x^2 + 9x g(x)=3xg(x) = 3x Write your answer as a polynomial or a rational function in simplest form. ______
Get tutor helpright-arrow

Posted 2 months ago

View all (128)