Inverse of Nonconstant Linear Functions
Read this topicExplanations 7
- Inverses are very interesting creations. You can think of them as things that you use to "undo" what you just did. Say, let's take the variable xxx and apply function fff to xxx…
By Joshua Pan, Jojo D, Joshua Siktar
- (Videos) Inverse Functions by PatrickJMT Here are some great video by PatrickJMT where he talks about what an inverse function is. An inverse function is a function that reverse…
By Alex Federspiel, Joshua Siktar
- (Video) How to Find the Inverse of a Function by Nancy Pi The general idea is that if a function y=f(x)y = f(x)y=f(x) has an inverse, you can find it by writing the equation as …
By Stefan Cuevas, Alex Federspiel, Joshua Siktar
- (Video) Inverse Functions by yaymath Here's a video by yaymath showing you how to find the inverse of a function. An inverse function is just the reverse of a function. A functi…
By Alex Federspiel
- (Video) Finding the Inverse of the Linear Function f(x)=x+2f(x)=x+2f(x)=x+2 by The Math Sorcerer In this video by The Math Sorcerer an example of finding the inverse of a linear…
By Stefan Cuevas, Alex Federspiel, Joshua Siktar
- What is an Inverse of a Linear Function? A function and its inverse undo each other. What exactly does that mean? Think of a function, often written like f(x)f\left(x\right)f(x)…
By Hannah Bonville, Alex Federspiel, Joshua Siktar
- Inverses occur in everyday life! Dirty dishes are washed to become new again. Borrowed library books are returned. The trip from school or work brings you back home. Functions t…
By Taylor Evans, Joshua Siktar
Problems 29
- What is the inverse function of f(x)=2x+1f(x) = 2x +1f(x)=2x+1?
- Suppose that a linear function has slope −5-5−5. What would be the slope of its inverse function?
- Find the inverse function of f(x)=4−8xf(x) = 4 - 8xf(x)=4−8x.
- Find the inverse function. f(x)=4x−5f(x)=4x-5f(x)=4x−5
- Find the inverse function. f(x)=8−3x13f(x)=\frac{8-3x}{13}f(x)=138−3x
- Find the inverse function. f(x)=−x−1−2f(x)=\frac{-x-1}{-2}f(x)=−2−x−1
- Find the inverse function. f(x)=3x7f(x)=\frac{3x}{7}f(x)=73x
- Let f(x)=2x+8f(x) = 2x + 8f(x)=2x+8. What is f−1f^{-1}f−1?
- Let f(x)=5x−3f(x) = 5x - 3f(x)=5x−3. What is f−1(37)f^{-1}(37)f−1(37)?
- Let fff be a function of the form f(x)=ax+bf(x) = ax + bf(x)=ax+b. If f=f−1f = f^{-1}f=f−1, and a≠−1a\ne -1a=−1, then what are the values of aaa and bbb?
- Fix b∈Rb \in \mathbb{R}b∈R. For all z∈Rz \in \mathbb{R}z∈R such that z≠−1,0,1,z \neq -1, 0, 1,z=−1,0,1, define a function fzf_zfz such that fz(x)=zx+bf_z(x) = zx + bfz(x)=zx+…
- What is the inverse of f(x)=3x+18f(x)=3x+18f(x)=3x+18?
- True or False\text{True or False}True or False === If aaa and bbb are real numbers greater than 000 and f(x)=ax+bf(x)=ax+bf(x)=ax+b then f−1(x)=1ax−baf^{-1}(x)=\frac1{a}x-\frac{…
- Which of the functions above is the inverse of f(x)=13x−2f(x)=\frac13x-2f(x)=31x−2?
- Find the inverse of f(x)=−7x+5−2.f(x) = \frac{-7x+5}{-2}.f(x)=−2−7x+5.
- Given the following (x,y)(x,y)(x,y) points, find the inverse equation of the function: (−2,2),(−1,3),(0,4),(1,5)(-2,2),(-1,3),(0,4),(1,5)(−2,2),(−1,3),(0,4),(1,5)
- What is the first step in solving for the inverse of a linear function?
- What is the last step in solving for the inverse of a linear function?
- Consider the picture above. What belongs in place of the question mark?
- Find the inverse function. f(x)=6.7x+2.35.8f\left(x\right)=\frac{6.7x+2.3}{5.8}f(x)=5.86.7x+2.3
- What belongs in place of the question mark?
- Find the inverse function. f(x)=10x3−16f\left(x\right)=\frac{10x}{3}-\frac{1}{6}f(x)=310x−61
- Consider the general form for a linear function f(x)=ax+bf\left(x\right)=ax+bf(x)=ax+b. Determine the form of the inverse function.
- Find the inverse of the function. f(x)=2x+1f(x)=2x+1f(x)=2x+1
- Find the inverse function. f(x)=6x−22x+1f\left(x\right)=\frac{6x-2}{2x+1}f(x)=2x+16x−2
- Find the inverse function. f(x)=x+9−4f\left(x\right)=\sqrt{x+9}-4f(x)=x+9−4
- Find the inverse function. f(x)=x−33−5f(x)=\sqrt[3]{x-3}-5f(x)=3x−3−5
- Let fff and ggg be functions with inverses such that f(x)=3g(x).f(x) = 3g(x).f(x)=3g(x). Which of the following is true?
- Let fff and ggg be invertible functions such that f(x)=3g(x).f(x) = 3g(x).f(x)=3g(x). Which of the following is true?