a. Find the formula for the inverse of the function f.

b. If the inverse is

Bergen
2021-09-07
Answered

Using data from 2009 through 2015, the percent of households with internet access in a certain region can be modeled by the function $f\left(x\right)=51.952{x}^{0.16}$ to the number of years after 2005.

a. Find the formula for the inverse of the function f.

b. If the inverse is$f}^{-1$ , find ${f}^{-1}.\left(f\left(20\right)\right)$

a. Find the formula for the inverse of the function f.

b. If the inverse is

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un4t5o4v

Answered 2021-09-08
Author has **105** answers

Step 1

Solve for function inverse

Step 2

$f\left(x\right)=51.952{x}^{0.160}$

Now$x=51.952{\left[f\left(x\right)\right]}^{0.160}$

$\frac{x}{51.952}={\left[f\left(x\right)\right]}^{0.160}$

${\left[\frac{x}{51.952}\right]}^{\frac{1}{0.160}}=f\left(x\right)$

Now$f}^{-1}\left(x\right)={\left(\frac{x}{51.952}\right)}^{\frac{1}{0.160}$

a)$F}^{-1}\left(x\right)={\left(\frac{x}{51.952}\right)}^{\frac{1}{0.160}$

b)${F}^{-1}\left(F\left(20\right)\right)={F}^{-1}\left(51.952{\left(20\right)}^{0.160}\right)$

$={\left(\frac{51.952{\left(20\right)}^{0.160}}{51.952}\right)}^{\frac{1}{0.160}}$

$={\left[{\left(20\right)}^{0.160}\right]}^{\frac{1}{0.160}}$

${f}^{-1}\left(f\left(20\right)\right)=20$

Solve for function inverse

Step 2

Now

Now

a)

b)

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