To find the inverse function F⁻¹(x):

Question

ScanSolve AI Tutor · Accepted Answer

Here are the inverse functions for each part. To find the inverse function F⁻¹(x): 1. Replace F(x) with y. 2. Swap x and y. 3. Solve the new equation for y. 4. Replace y with F⁻¹(x). a) F(x) = x+2 Step 1: Replace F(x) with y. y = x+2 Step 2: Swap x and y. x = y+2 Step 3: Solve for y. y = x−2 Step 4: Replace y with F⁻¹(x). F⁻¹(x) = x−2; The inverse function is F⁻¹(x) = x−2. b) F(x) = x−7 Step 1: Replace F(x) with y. y = x−7 Step 2: Swap x and y. x = y−7 Step 3: Solve for y. y = x+7 Step 4: Replace y with F⁻¹(x). F⁻¹(x) = x+7; The inverse function is F⁻¹(x) = x+7. c) F(x) = 22+x Step 1: Replace F(x) with y. y = 22+x Step 2: Swap x and y. x = 22+y Step 3: Solve for y. y = x−22 Step 4: Replace y with F⁻¹(x). F⁻¹(x) = x−22; The inverse function is F⁻¹(x) = x−22. e) F(x) = 3x Step 1: Replace F(x) with y. y = 3x Step 2: Swap x and y. x = 3y Step 3: Solve for y. y = x/3 Step 4: Replace y with F⁻¹(x). F⁻¹(x) = x/3; The inverse function is F⁻¹(x) = x/3. f) F(x) = 8x Step 1: Replace F(x) with y. y = 8x Step 2: Swap x and y. x = 8y Step 3: Solve for y. y = x/8 Step 4: Replace y with F⁻¹(x). F⁻¹(x) = x/8; The inverse function is F⁻¹(x) = x/8. g) F(x) = x/4 Step 1: Replace F(x) with y. y = x/4 Step 2: Swap x and y. x = y/4 Step 3: Solve for y. y = 4x Step 4: Replace y with F⁻¹(x). F⁻¹(x) = 4x; The inverse function is F⁻¹(x) = 4x.

To find the inverse function F⁻¹(x):

Answers

Step-by-step solution

Part a· 4 steps

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part b· 4 steps
$F^{-1}(x) = x+7$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part c· 4 steps
$F^{-1}(x) = x-22$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part e· 4 steps
$F^{-1}(x) = \frac{x}{3}$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part f· 4 steps
$F^{-1}(x) = \frac{x}{8}$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part g· 4 steps
$F^{-1}(x) = 4x$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

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To find the inverse function F⁻¹(x):

Answers

Step-by-step solution

Part a· 4 steps

Replace F(x)F(x)F(x) with yyy.

Swap xxx and yyy.

Solve for yyy.

Replace yyy with F−1(x)F^{-1}(x)F−1(x).

Part b· 4 stepsF−1(x)=x+7F^{-1}(x) = x+7F−1(x)=x+7

Replace F(x)F(x)F(x) with yyy.

Swap xxx and yyy.

Solve for yyy.

Replace yyy with F−1(x)F^{-1}(x)F−1(x).

Part c· 4 stepsF−1(x)=x−22F^{-1}(x) = x-22F−1(x)=x−22

Replace F(x)F(x)F(x) with yyy.

Swap xxx and yyy.

Solve for yyy.

Replace yyy with F−1(x)F^{-1}(x)F−1(x).

Part e· 4 stepsF−1(x)=x3F^{-1}(x) = \frac{x}{3}F−1(x)=3x​

Replace F(x)F(x)F(x) with yyy.

Swap xxx and yyy.

Solve for yyy.

Replace yyy with F−1(x)F^{-1}(x)F−1(x).

Part f· 4 stepsF−1(x)=x8F^{-1}(x) = \frac{x}{8}F−1(x)=8x​

Replace F(x)F(x)F(x) with yyy.

Swap xxx and yyy.

Solve for yyy.

Replace yyy with F−1(x)F^{-1}(x)F−1(x).

Part g· 4 stepsF−1(x)=4xF^{-1}(x) = 4xF−1(x)=4x

Replace F(x)F(x)F(x) with yyy.

Swap xxx and yyy.

Solve for yyy.

Replace yyy with F−1(x)F^{-1}(x)F−1(x).

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Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part b· 4 steps
$F^{-1}(x) = x+7$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part c· 4 steps
$F^{-1}(x) = x-22$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part e· 4 steps
$F^{-1}(x) = \frac{x}{3}$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part f· 4 steps
$F^{-1}(x) = \frac{x}{8}$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .

Part g· 4 steps
$F^{-1}(x) = 4x$

Replace $F(x)$ with $y$ .

Swap $x$ and $y$ .

Solve for $y$ .

Replace $y$ with $F^{-1}(x)$ .