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 {:[f(x)=(3+4x)/(1-5x)?],[f^(-1)(x)=]:}

What is the inverse of the function\newlinef(x)=3+4x1−5x?f−1(x)=□ \begin{array}{l} f(x)=\frac{3+4 x}{1-5 x} ? \\ f^{-1}(x)=\square \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Identify inverse functionsright chevron icon

Full solution

Q. What is the inverse of the function\newlinef(x)=3+4x1−5x?f−1(x)=□ \begin{array}{l} f(x)=\frac{3+4 x}{1-5 x} ? \\ f^{-1}(x)=\square \end{array}
  1. Switching roles and setting up the equation: To find the inverse of the function f(x)=3+4x1−5xf(x) = \frac{3+4x}{1-5x}, we need to switch the roles of xx and f(x)f(x) and then solve for the new xx. Let y=f(x)y = f(x), so we have y=3+4x1−5xy = \frac{3+4x}{1-5x}. Now we replace f(x)f(x) with xx and xx with yy to find the inverse function xx00: xx11.
  2. Multiplying both sides to eliminate the fraction: Next, we solve for yy in terms of xx. To do this, we multiply both sides of the equation by (1−5y)(1-5y) to get rid of the fraction:\newlinex(1−5y)=3+4y.x(1-5y) = 3+4y.
  3. Distributing and rearranging the equation: Now we distribute xx on the left side of the equation: x−5xy=3+4yx - 5xy = 3 + 4y.
  4. Isolating y and factoring out: We want to isolate y, so we'll move all terms involving y to one side and the constant to the other side: 5xy−4y=x−35xy - 4y = x - 3.
  5. Dividing both sides to solve for yy: Factor out yy from the left side of the equation:\newliney(5x−4)=x−3y(5x - 4) = x - 3.
  6. Finding the inverse function: Now, divide both sides by (5x−4)(5x - 4) to solve for yy:y=x−35x−4.y = \frac{x - 3}{5x - 4}.
  7. Finding the inverse function: Now, divide both sides by (5x−4)(5x - 4) to solve for yy:y=x−35x−4y = \frac{x - 3}{5x - 4}.We have found the inverse function. The inverse of f(x)=3+4x1−5xf(x) = \frac{3+4x}{1-5x} is f−1(x)=x−35x−4f^{-1}(x) = \frac{x - 3}{5x - 4}.

More problems from Identify inverse functions

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 (22)