Chapter 2 Test

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2 Test

Chapter 2 test is also our review content.

[Eigenvalue]

2. f(x)=[tex]\sqrt{4x-5}[/tex]
4x-5[tex]\ge[/tex]0, as the radicand of a real number cannot be negative
4x[tex]\ge[/tex]5
x[tex]\ge \frac{5}{4}[/tex]

2[tex]\frac{1}{2}[/tex]. To find the inverse, let f(x)=y, and switch the x and y values

x=[tex]\sqrt{4y-5}[/tex]
Square both sides: x²=4y-5
x²+5=4y
y=[tex]\frac{x²+5}{4}[/tex]
As the range of f(x) is greater than or equal to 0, the domain of [tex]f^{-1}[/tex](x) is greater than or equal to 0; the domain of a function becomes the range of its inverse, and vice versa.

As x[tex]\ge[/tex]0, y[tex]\ge \frac{5}{4}[/tex]

[nycmath]

2. f(x)=[tex]\sqrt{4x-5}[/tex]
4x-5[tex]\ge[/tex]0, as the radicand of a real number cannot be negative
4x[tex]\ge[/tex]5
x[tex]\ge \frac{5}{4}[/tex]

2[tex]\frac{1}{2}[/tex]. To find the inverse, let f(x)=y, and switch the x and y values

x=[tex]\sqrt{4y-5}[/tex]
Square both sides: x²=4y-5
x²+5=4y
y=[tex]\frac{x²+5}{4}[/tex]
As the range of f(x) is greater than or equal to 0, the domain of [tex]f^{-1}[/tex](x) is greater than or equal to 0; the domain of a function becomes the range of its inverse, and vice versa.

As x[tex]\ge[/tex]0, y[tex]\ge \frac{5}{4}[/tex]

Is this the work for question 2?

[Eigenvalue]

2. f(x)=[tex]\sqrt{4x-5}[/tex]
4x-5[tex]\ge[/tex]0, as the radicand of a real number cannot be negative
4x[tex]\ge[/tex]5
x[tex]\ge \frac{5}{4}[/tex]

2[tex]\frac{1}{2}[/tex]. To find the inverse, let f(x)=y, and switch the x and y values

x=[tex]\sqrt{4y-5}[/tex]
Square both sides: x²=4y-5
x²+5=4y
y=[tex]\frac{x²+5}{4}[/tex]
As the range of f(x) is greater than or equal to 0, the domain of [tex]f^{-1}[/tex](x) is greater than or equal to 0; the domain of a function becomes the range of its inverse, and vice versa.

As x[tex]\ge[/tex]0, y[tex]\ge \frac{5}{4}[/tex]

Is this the work for question 2?

Yes, this the work for question 2.

[nycmath]

2. f(x)=[tex]\sqrt{4x-5}[/tex]
4x-5[tex]\ge[/tex]0, as the radicand of a real number cannot be negative
4x[tex]\ge[/tex]5
x[tex]\ge \frac{5}{4}[/tex]

2[tex]\frac{1}{2}[/tex]. To find the inverse, let f(x)=y, and switch the x and y values

x=[tex]\sqrt{4y-5}[/tex]
Square both sides: x²=4y-5
x²+5=4y
y=[tex]\frac{x²+5}{4}[/tex]
As the range of f(x) is greater than or equal to 0, the domain of [tex]f^{-1}[/tex](x) is greater than or equal to 0; the domain of a function becomes the range of its inverse, and vice versa.

As x[tex]\ge[/tex]0, y[tex]\ge \frac{5}{4}[/tex]

Is this the work for question 2?

Yes, this the work for question 2.

Great.

[Eigenvalue]

Question 8:

[Eigenvalue]

Question 4:

[nycmath]

Question 8:

Cool