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:

What is the inverse of the function {:[h(x)=(3-x)/(x+1)" ? "],[h^(-1)(x)=◻]:}

What is the inverse of the function h(x)=3−xx+1 h(x) = \frac{3-x}{x+1} ? h−1(x)=□ h^{-1}(x) = \square

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find the vertex of the transformed functionright chevron icon

Full solution

Q. What is the inverse of the function h(x)=3−xx+1 h(x) = \frac{3-x}{x+1} ? h−1(x)=□ h^{-1}(x) = \square
  1. Understand Inverse Function: Understand the concept of an inverse function. An inverse function, denoted as h−1(x)h^{-1}(x), is a function that reverses the effect of the original function h(x)h(x). To find the inverse, we swap the roles of xx and yy in the original function and then solve for yy.
  2. Write Original Function: Write the original function with yy instead of h(x)h(x). Let y=3−xx+1y = \frac{3-x}{x+1}. We will solve for xx in terms of yy to find the inverse function.
  3. Swap xx and yy: Swap xx and yy to find the inverse.\newlineReplace yy with xx and xx with yy to get the equation for the inverse function: x=3−yy+1x = \frac{3-y}{y+1}.
  4. Solve for y: Solve for y in terms of x.\newlineTo find y, we need to isolate it on one side of the equation. Start by multiplying both sides by (y+1)(y+1) to get rid of the denominator: x(y+1)=3−yx(y+1) = 3-y.
  5. Distribute xx: Distribute xx on the left side of the equation.xy+x=3−yxy + x = 3 - y.
  6. Move Terms: Move all terms involving yy to one side and the constant terms to the other side.\newlineAdd yy to both sides and subtract xx from both sides to get: xy+y=3−xxy + y = 3 - x.
  7. Factor out yy: Factor out yy on the left side of the equation.y(x+1)=3−x.y(x + 1) = 3 - x.
  8. Divide for yy: Divide both sides by (x+1)(x + 1) to solve for yy.y=3−xx+1y = \frac{3 - x}{x + 1}.
  9. Write Inverse Function: Write the inverse function.\newlineThe inverse function is h−1(x)=3−xx+1h^{-1}(x) = \frac{3 - x}{x + 1}.

More problems from Find the vertex of the transformed function

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 8 months 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 7 months 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 5 months 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 5 months 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 5 months 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 5 months 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 5 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 4 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 4 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 5 months ago

View all (123)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant