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:

y=x2+7x−5y=x^2+7x-5 make xx the subject

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. y=x2+7x−5y=x^2+7x-5 make xx the subject
  1. Move constant term: To isolate xx, we need to complete the square. First, move the constant term to the other side of the equation by adding 55 to both sides.\newliney+5=x2+7xy + 5 = x^2 + 7x
  2. Complete the square: Now, to complete the square, we need to add and subtract (b2)2(\frac{b}{2})^2, where bb is the coefficient of xx. In this case, b=7b = 7, so (72)2=494(\frac{7}{2})^2 = \frac{49}{4}.y+5+494=x2+7x+494y + 5 + \frac{49}{4} = x^2 + 7x + \frac{49}{4}
  3. Subtract 494\frac{49}{4}: Subtract 494\frac{49}{4} from both sides to keep the equation balanced.\newliney+5−494=x2+7x+494−494y + 5 - \frac{49}{4} = x^2 + 7x + \frac{49}{4} - \frac{49}{4}
  4. Simplify left side: Simplify the left side of the equation. y+204−494=(x+72)2y + \frac{20}{4} - \frac{49}{4} = (x + \frac{7}{2})^2
  5. Combine terms: Combine the terms on the left side. y−294=(x+72)2y - \frac{29}{4} = (x + \frac{7}{2})^2
  6. Take square root: Take the square root of both sides to solve for xx.±y−294=x+72\pm\sqrt{y - \frac{29}{4}} = x + \frac{7}{2}
  7. Subtract 72\frac{7}{2}: Subtract 72\frac{7}{2} from both sides to isolate xx.\newlinex=±y−294−72x = \pm\sqrt{y - \frac{29}{4}} - \frac{7}{2}

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)