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Find the inverse of f. Determine the domain and range of each resulting inverse functions.
3. f(x) = x+2
Solution:

Domain
Range

4. f(x) = x² + 2
Solution:

Domain
Range

5. f(x) = √1+xX
Solution:

Domain
Range​

Find The Inverse Of F Determine The Domain And Range Of Each Resulting Inverse Functions3 Fx X2Solution Domain Range 4 Fx X 2 SolutionDomain Range 5 Fx 1xX Solu class=

Sagot :

Step-by-step explanation:

Find the inverse of f. Determine the domain and range of each resulting inverse functions.

3. f(x) = x+2

Solution:

Domain

Range

4. f(x) = x² + 2

Solution:

Domain

Range

5. f(x) = √1+xX

Solution:

Domain

RangeFind the inverse of f. Determine the domain and range of each resulting inverse functions.

3. f(x) = x+2

Solution:

Domain

Range

4. f(x) = x² + 2

Solution:

Domain

Range

5. f(x) = √1+xX

Solution:

Domain

Range

XHephaestusidn

Find the inverse of f. Determine the domain and range of each resulting inverse functions.

3. f(x) = x+2

Solution:

y = x+2

interchange x and y;

x = y+2

subtract 2 to both sides of the equation;

x-2 = y

rewrite y as f^-1(x);

[tex]Answer = f^-1(x) = x-2[/tex]

[tex]Domain = {X|x∈ℝ}[/tex]

[tex]Range = {X|x∈ℝ}[/tex]

4. f(x) = x² + 2

Solution:

y = x² + 2

interchange x and y;

x = y² + 2

subtract 2 to both sides of the equation;

x-2 = y²

take the square root of both sides of the equation;

√(x-2) = √(y)²

the square root and the 2 power degree of y will negate;

y = √(x-2)

rewrite y as f^-1(x);

[tex]Answer = f^-1(x) = \sqrt{(x-2)}[/tex]

[tex]Domain = {X| x \geqslant 2}[/tex]

[tex]Range \: = Y|y \geqslant 0[/tex]

5. f(x) = √1+x

Solution:

y = √1+x

interchange x and y;

x = √1+y

square both sides of the equation;

x² = 1+y

subtract 1 to both sides of the equation;

x²-1 = y

rewrite y as f^-1(x);

[tex]Answer = f^-1(x) = x²-1[/tex]

[tex]Domain=X∣x∈R[/tex]

[tex]Range = Y|y≥-1[/tex]

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