# Tagged Questions

3answers
91 views

### What is the best way to find $g(x) = f^{-1}(x)$?

so the problem I have is if $f(x) = \sqrt{x+3} - 2$ and it asks to find the solution of $f(x) = f^{-1}(x)$. So i know to find the inverse, which I got as $f^{-1}(x) = (x+2)^2-3$. So to find the ...
0answers
58 views

### How to find the inverse function of f(x)=x+sin(x)-a

The problem is how to find the inverse function of $$f(x)=x+\sin(x)-a$$ where $a$ is real parameter. I tried to write $\sin(x)$ as $\frac{i}{2}(e^{-ix}-e^{ix})$. Problem is how to solve this equation: ...
1answer
27 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.
7answers
613 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?
4answers
80 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 ...
1answer
46 views

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 $[-3, 3]$.
0answers
85 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 ...
2answers
82 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 ...
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 : ...
3answers
224 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 $x = 0$ ?
1answer
92 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 ...
1answer
181 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 ...
5answers
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: ...