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)/(4)x+12?],[h^(-1)(x)=]:}

What is the inverse of the function h(x)=34x+12 h(x) = \frac{3}{4}x + 12 ? h−1(x)= h^{-1}(x) =

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 h(x)=34x+12 h(x) = \frac{3}{4}x + 12 ? h−1(x)= h^{-1}(x) =
  1. Rewriting h(x)h(x) as yy: To find the inverse of the function h(x)h(x), we need to switch the roles of xx and yy and then solve for yy. Let's start by rewriting h(x)h(x) as yy:\newliney=(34)x+12y = \left(\frac{3}{4}\right)x + 12
  2. Switching x and y: Now, we switch x and y to find the inverse:\newlinex=34y+12x = \frac{3}{4}y + 12
  3. Isolating y: Next, we solve for y by isolating it on one side of the equation. First, we subtract 1212 from both sides:\newlinex−12=(34)yx - 12 = \left(\frac{3}{4}\right)y
  4. Solving for y: Now, we multiply both sides by the reciprocal of (34)(\frac{3}{4}), which is (43)(\frac{4}{3}), to solve for y:\newline(43)(x−12)=y(\frac{4}{3})(x - 12) = y
  5. Simplifying the equation: Simplify the equation to get the inverse function:\newliney = 43x−16\frac{4}{3}x - 16\newlineThis is the inverse function, which we denote as h−1(x)h^{-1}(x):\newlineh−1(x)=43x−16h^{-1}(x) = \frac{4}{3}x - 16

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 3 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 2 months 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 2 months 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 2 months 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 3 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 2 months 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 2 months 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 2 months 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 2 months 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 3 months ago

View all (22)