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:

Find the inverse of \newlinef(x)=14x−7f(x)=\frac{1}{4x}-7

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives using the chain rule IIright chevron icon

Full solution

Q. Find the inverse of \newlinef(x)=14x−7f(x)=\frac{1}{4x}-7
  1. Set f(x)f(x) equal to yy: Set f(x)f(x) equal to yy.y=14x−7y = \frac{1}{4x} - 7
  2. Swap x and y: Swap x and y to find the inverse.\newlinex=14y−7x = \frac{1}{4y} - 7
  3. Solve for y: Solve for y.\newlinex+7=14yx + 7 = \frac{1}{4y}
  4. Multiply by 4y4y: Multiply both sides by 4y4y to get rid of the fraction.\newline4y(x+7)=14y(x + 7) = 1
  5. Distribute 4y4y: Distribute 4y4y on the left side.4yx+28y=14yx + 28y = 1
  6. Isolate y: Isolate y on one side.\newline28y=1−4yx28y = 1 - 4yx
  7. Factor out y: Factor out y from the left side.\newliney(28+4x)=1y(28 + 4x) = 1
  8. Divide both sides: Divide both sides by (28+4x)(28 + 4x) to solve for yy.y=1(28+4x)y = \frac{1}{(28 + 4x)}
  9. Write final expression: Write the final expression for the inverse function. f−1(x)=1(28+4x)f^{-1}(x) = \frac{1}{(28 + 4x)}

More problems from Find derivatives using the chain rule II

Question
Find the derivative of f(x) f(x) .\newlinef(x)=cos⁡(x) f(x) = \cos(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡(x) f(x) = \tan(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ex f(x) = e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ln⁡(x) f(x) = \ln(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=xex f(x) = x e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=exx f(x) = \frac{e^x}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) . \newline f(x)=e(x+1) f(x) = e^{(x + 1)} \newline f′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=x+3 f(x) = \sqrt{x+3} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of g(x) g(x). \newline g(x)=ln⁡(2x) g(x) = \ln(2x) \newline g′(x)= g^{\prime}(x) = ______
Get tutor helpright-arrow

Posted 3 months ago

View all (17)