How to find the inverse of a function with e

Asked by admin @ 05/11/2021 in Mathematics viewed by 240 People

F(x)=e^2x-4
Determine inverse of given function

Answered by admin @ 05/11/2021

Answer:

$f^{-1}(x)=\frac{1}{2}ln(x)+2$

Step-by-step explanation:

Start by changing the f(x) into a y. Then switch the x and the y. Then solve for the new y. Like this:

$y=e^{2x-4}$ becomes

$x=e^{2y-4}$

To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides. Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.

$ln(x)=ln(e)^{2y-4}$

When the ln and the e cancel out we are left with

ln(x) = 2y - 4. Add 4 to both sides to get

ln(x) + 4 = 2y. Divide both sides by 2 to get

$\frac{1}{2}ln(x) + 4 = y$ .

Since that is the inverse of y, we can change the y into inverse function notation:

$f^{-1}(x)=\frac{1}{2}ln(x)+4$

Find the elasticity of demand e for the demand function

Asked by admin @ 05/11/2021 in Mathematics viewed by 292 persons

For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. (Round your answer to three decimal …

Find the derivative of the function by the limit process

Asked by admin @ 04/12/2021 in Mathematics viewed by 356 persons

Find the derivative of the following function using the limit process

Find average rate of change of function over given interval

Asked by admin @ 02/12/2021 in Mathematics viewed by 327 persons

Calculate the average rate of change over the interval [1, 3] for the following function. F(x)=4(5)^x

How to find end behavior of a function without graphing

Asked by admin @ 01/12/2021 in Mathematics viewed by 311 persons

Without graphing, describe the end behavior of the graph of the function. (Image provided includes function and answer options) *Please show all work, thanks.*

Finding the domain and range of a square root function

Asked by admin @ 29/11/2021 in Mathematics viewed by 359 persons

How do you find domain and range of a square root function

How to find x and y intercepts of rational functions

Asked by admin @ 27/11/2021 in Mathematics viewed by 329 persons

How do we find x-intercept of rational function

Find an equation for f 1 x the inverse function

Asked by admin @ 27/11/2021 in Mathematics viewed by 295 persons

Find the inverse function F -1 (X) for the given function F (X)

Finding the equation of an exponential function from a graph

Asked by admin @ 26/11/2021 in Mathematics viewed by 318 persons

Write an equation for the exponential function represented in the table and graph below.

How do you find the parent function of a graph

Asked by admin @ 26/11/2021 in Mathematics viewed by 283 persons

Name a parent function where the graph is shaped like the letter "u". Name a parent function where the graph is shaped like the letter "v"?

How do you find the domain of a piecewise function

Asked by admin @ 26/11/2021 in Mathematics viewed by 289 persons

Find the domain of the following piecewise function

How do you find the domain of a composite function

Asked by admin @ 26/11/2021 in Mathematics viewed by 277 persons

Find the domain of the composite function (fog)(x) where f(x) = 6x + 30; g(x) = the square root of x

How to find the horizontal asymptote of a rational function

Asked by admin @ 25/11/2021 in Mathematics viewed by 279 persons

State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote. (5 points) f(x)= x^2+3x-2/x-2