0
votes
1answer
26 views

Plotting the inverse of a function

The inverse of the function $y=2^x$ is $\bf (A)$ $y=\log_2x\quad{\bf (B)}\, y=-2^x\quad{\bf (C)}\,y=2^{-x}\quad{\bf (D)}\,y=x^2.$ Need help solving this problem and plotting it on a graph.
2
votes
7answers
589 views

How to find the inverse of the function?

$$f(x)=\frac{x+2}{5x-1}$$ Answer: $$f^{-1}(x)=\frac{x+2}{5x-1}$$ Can one of you explain how the inverse is the same exact thing as the original equation?
2
votes
4answers
73 views

Finding the inverse of $f(x)=|x|-2$

How would I find the inverse of the function $f(x)=|x|-2$? I have swapped $x$ and $y$, and tried to isolate $y$, reaching up to $x+2=|y|$ Whenever I see absolute values, I always break the problem up ...
2
votes
1answer
44 views

Inverse function of $f(t)=5 +\frac{75}{1 + e^{-((t-50)/10)}}$

i need to find the inverse function of $$ v= f(t)=5 + \frac{75}{1 + e^{-\frac{t-50}{10}}} $$ so far i have $$ v - 5 = \frac{75}{1 + e^{-\frac{t-50}{10}}} $$ $$ (v-5) \left(1 + ...
1
vote
3answers
58 views

Algebra question: Finding inverse function

This question is about finding the inverse function of $f(x)=-\sqrt{9-x^2}$ I seem to be making an error with one of the manipulations. Here is my attempt. $$x=-\sqrt{9-y^2}$$ ...
2
votes
2answers
57 views

Find the inverse of $f(x) = (x+1)/(x-8)$

Find the inverse of this function: I have gotten this far: $x = y+1/y-8$ $x(y-8) = y+1$ $x(y-8)-1=y$ $xy-8x - 1 = y$ I think I went backwards?
1
vote
0answers
34 views

Finding the inverse of trig functions

I'm supposed to find the inverse of $$f(x) = \cos(x)+x$$ I usually just substitute $x$ for $y$ and then re-arrange. What do I do in this scenario?
1
vote
1answer
23 views

function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
1
vote
2answers
1k views

Inverse of function, containing a fraction

This is basic, I know, but I cannot seem to come up with the right answer. Find the inverse of the function: $$f(x)= \frac3{x+1}$$ My steps: 1. Convert f(x) to y $$y = \frac3{x+1}$$ Switch places ...
2
votes
4answers
98 views

Inverse of $(e^x - e^{-x})/2$

What is the inverse of the function $f(x)=\frac{e^x - e^{-x}}2$? I tried replacing $e^x$ by a variable but I still can't get it.
0
votes
2answers
68 views

Inverse of $f(x) = 18sin(\frac{x\pi}{7})+20$

This is an exercise taken from Mooculus-textbook (page 17, exercise 5 to be exact). The task given is to find an inverse for $f(x) = 18\sin(\frac{x\pi}{7})+20$ (restricting domain to $[3.5,10.5]$) ...
0
votes
1answer
54 views

Maximal value of domain for a function by looking at inverse function.

The function g:[–a,a]→ R, g(x)=sin(2(x-π/6))has an inverse function.The maximum possible value of a is: From what I understand the domain of g(x) is the range of g'(x). So I would try to find the ...
1
vote
2answers
35 views

Show that this is one to one continuous and find its inverse which is continuous as well.

Let's define $\phi: \Bbb R^2 \to S$ for $S$ is subset of $\Bbb R^3$ For constant $a,b,c,d$ and $c\not =0$ $$\phi(x,y)=(x,y, \frac{d-ax-by}{c})$$ I want to show that the function $\phi$ is 1-1 ...
0
votes
1answer
57 views

Calculating Inverse function

Please help me with the following question: Calculate, if possible, the inverse of the following functions: (i) $f(x) = (2x - 2)^5$ (ii) $f(x) = (2x - 3)/4$ (iii) $f(x) = x^2 + 1,$ for $ x \geq ...
1
vote
2answers
69 views

Finding inverse of functions[methods of]

I am now trying to understand functions, inverses and composites. I must admit am not getting a thing. But following some leads, I managed to work one as below. Is this a good understanding on hows ...
0
votes
2answers
372 views

Find the Inverse function of f. $f(x)=1+\sqrt{1+x}$

I found the Inverse of the function, $f^{-1}(x)= x^2-2x$. The back of my pre-cal book gives me the inverse of the function and the domain. What I don't understand is, how the domain comes to be $x ...
3
votes
3answers
173 views

Is $\sqrt{x^2}$ always $\pm x?$

I am wondering if this holds in every single case: $$\sqrt{x^2} = \pm x$$ Specifically in this case: $$\sqrt{\left(\frac{1}{4}\right)^2}$$ In this one we know that the number is positive before ...
-2
votes
2answers
52 views

Sketching the Inverse of a Function [closed]

I can't figure out how to sketch $f^{-1}$ if $f$ has the domain of $[-3, 3]$.
1
vote
0answers
84 views

General solution for $M^{\circ -1 }(y)=x $ when $g(x)e^{f(x) }=y$

Reading this question $e^{C/x }-1=D/(x + a) $, i found my self completely unable to do anything. This is much more hard for me than my easy exercises about Lambert $W$-function. So I probably need ...
0
votes
2answers
81 views

Need help with inverse laplace transform problem

I'm really stuck this problem. This actually resulted because of equations for a circuit analysis problem, so in case it would help I'll list the equations here too. Although, feel free to ignore ...
0
votes
1answer
40 views

Algorithm for root function $[2^{n-1}]$

I am attempting to convert this function $[2^{n-1}]$ into a root function to return original value. Thus far all my attempts have ended in abject failure. Base : 1 2 3 4 5 6 7 8 9 Result : ...
1
vote
3answers
188 views

Is the inverse of a function the reflection of the function about the line $y=x$?

So if we have $f(x)$: $y=x$ when $x \ne 1$ and $y = 0$ when $x = 1$. The inverse would be: $y=x$ when $x \ne 0$ and $y=1$ when $x = 0$ ?
3
votes
1answer
91 views

Find whether or not an inverse exists algebraically

Is there an algebraic(without graphs) way to determine the existence of a function's inverse without using calculus? I'm an undergrad engineer and can obviously solve this using basic calculus, but ...
0
votes
1answer
159 views

Walk me through step by step on inverse problem

This is the problem that I am having trouble with for my test review. I am completely blank and don't know what it is asking for. Can you please guide me step by step. For example: Why did constant k ...
0
votes
4answers
3k views

Finding the inverse of $h(x) = 3^x$

most of the time I know how to find the inverse of a function (make it equal $y$, solve for $x$ and then swap $x$ and $y$), but I have no idea how to do that for this one, so any help would be great: ...