Finding the inverse function of y= ln(x+3)?
To find the inverse function of an equation you start by switching the x and the y and then you solve for y. So: x = ln(y+3) e^x = e^(ln(y+3)) e^x = y+3 e^x - 3 = y y= e^x - 3 You can also check this by graphing the two and making sure that they mirror each other over the line y=x (that's part of the definition of inverse functions). Don't worry I've already checked it for you. ;) Hope that helps!
F(x)= 2x^3 +3 inverse function?
f(x)=2x³+3 is an increasing function thus it has inverse function. y=2x³+3 => x=³√[(y-3)/2] ∴f-1(x)=³√[(x-3)/2] or to be written as [(x-3)/2]^(1/3)
Help with inverse functions?
y=100*2^t/3 y/100=2^t/3 log(y/100)= t/3 log 2 [log(y/100)]/[log 2]=t/3 [log(y/100)]/[log 2]3=t Inverse Function of f[t]=100*2^t/3 is: f^(-1)(t)=3([log(t/100)]/[log 2]) or y^(-1)(t)=3([log(t/100)]/[log 2])
What is an inverse function?
An inverse function([math]f^{-1}[/math] )is a function that reverses what another function ([math]f[/math]) did to any valid input value.For example, let us say that you have the function [math]y=f(x)=x^2[/math]. Now let us say that you feed in the number x = 5.[math]f(5) = 5^2 = 25[/math]Now, the inverse of the f(x) is known to be [math]f^{-1}(x) = \pm \sqrt{x}[/math]Let us now plug in 25 ( the output of the original function) into the input of the inverse function.[math]f^{-1}(25) = \pm \sqrt{25} = \pm 5[/math]Note that the inverse function gave us two values. This is because plugging in either -5 and 5 to the original function gives us 25. So, the inverse function has “undone” what the original function had done. That is what an inverse function is.Some examples are listed below:[math]f(x) = sin(x), g(x) = arcsin(x)[/math][math]f(x) = e^x, g(x) = log_e(x)[/math][math]f(x) = x, f(x) = x[/math]How do you actually find an inverse function?Generally you can write a function in the following form: [math]y = f(x)[/math]In order to find the inverse function of the function f(x), all you have to do is switch y and x and solve for y, if possible.I encourage you to try it with some of the functions indicated above.
Inverse Function of f(x) = 4x-1/2x+3?
Interchange x and y , then solve for y x=(4y-1)/(2y +3) x(2y+3) =4y-1 2xy +3x =4y -1 2xy -4y =-3x -1 y(2x-4) =-3x-1 y =(-3x-1) / (2x-4)
How do you find the inverse of an absolute value function?
y = -3|x + 1| + 4 x = -3|y + 1| + 4 x - 4 = -3|y + 1| (4 - x)/3 = |y + 1| ± (4 - x)/3 = y + 1 y = -1 ± (4 - x)/3 This is actually an inverse relation, not an inverse function. It can be rewritten as a piecewise function: y = -1 + (4 - x)/3 if x ≤ 4 and y = -1 + (x - 4)/3 if x < 4 The original function can be rewritten also: y = -3(x + 1) + 4 if x ≥ -1 and y = 3(x + 1) + 4 if x < -1
Help! can someone help me find the inverse of y=3log2x?
y = 3log 2x y/3 = log 2x 10^(y/3) = 2x x = 10^(y/3) / 2 y^-1 = 10^(x/3) / 2
How does one find the domain of an inverse function within an inverse function?
a) Similar to John Calligy ‘s explanation. The inner expression can take values between [-1,1]. So, the domain of the function f(x) is [-13, 7].b) To simplify the function without trigonometric functions..Assign sininv((x+3)/10) to theta. So, sin(theta) = (x+3)/10 and f(x) = tan(theta)Then tan(theta) = (x+3)/sqrt(100 - (x+3)^2) which is f(x)Its been long I looked at trigonometry. Please let me know if you find something incorrect.
Find the inverse function of f informally. Verify that f (f^ -1(x)) = x and f ^ -1(f(x)= x?
Having trouble with these problems.? Math I need help anyone be patient with me trying to understand? Find the inverse function of f informally. Verify that f (f^ -1(x)) = x and f ^ -1(f(x)= x 1. f(x) = 2x + 1 Show that f and g are inverse functions algebraically. 2. f(x) = x-9/ 4, g(x) = 4x + 9 Show that f and g are inverse fuctions algebraically Problems 3 & 4. 3. f(x) = x^3, g(x)= 3 sqaure root of x 4. f(x) = 1/1+x, x >_ 0; g(x) = 1 - x/ x, 0 < x < _ 1 Show that f and g are inverse functions (a) graphically and (b) numerically. 5. f (x) = 2x, g(x) = x/2 Determine algebraically whether the function is one-to-one. Verify your answer graphically Problems 6 & 7. 6. f(x)=3x + 5 7. f (x) = square root 2x+3 Find the inverse function of f algebraically. 8. f(x) = 3x 9. f(x) = square root 4 - x ^2, 0 _< x <_ 2 Last question Restrict the domain of the function f so that the function is one-to-one and has an inverse function. Then find the inverse function f ^ -1. State the domains and ranges of f and f^ -1. Explain your results. 10. f(x) = 1 - x ^4
Why do we solve for y when we're solving for the inverse of a function?
I believe you're asking why is it that when we swap and solve, we et the inverse. A function describes chanes done to the input to give you an output. An inverse of a function is taking you from the output, back to the input you originally gave. For example, f(x)=x+2 is a function that says add 2 to the input and you get your result. Let's replace f(x) with y. we get Y=x+2. Since when x is the input of the function, its output is Y. Then the inverse function should do the opposite, take in y, and give an x as he result. Then we need to solve for x to be by itself, we get x=y-2. You're used to having x as the input and Y as the output, so switch them around, y=x-2. It's worth to note that not all functions can have an inverse. Since some functions can take two different inputs and give you the same output, you can't really infer which input you had if you are given an output.For example, f(x)=|x|. f(1)=1 and f(-1)=1. How would you define an inverse for that? Let's say g(x) represents the inverse. What should g(1) give? 1? -1? It doesn't make sense to have an inverse.A more rigours explanation would require going into set theory, surjectivity, and objectivity of functions. Let me know If you would like me to go into detail about these.