Find Value of B

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

96. If f(x) = (2x - B)/(3x + 4) and f(2) = 1/2, what is the value of B?

NOTE:

This is the third precalculus question today. Tomorrow, I will post another set of three questions from Chapter 2, Section 2.1. However, later today, and tonight on my lunch break, I will post a few random questions in the other forums here to help keep our math skills sharp. However, only three precalculus questions per day moving forward in the College Algebra forum. This will lead to greater discussion for each question posted. Have a great day everyone.

nycmath

[Math Tutor]

Substitute [tex]x=2[/tex] into the function and set the result equal to [tex]\frac{1}{2}[/tex]:

[tex]f(2)=\frac{2(2)-B}{3(2)+4}=\frac{4-B}{10}=\frac{1}{2}[/tex]

Cross-multiply:

[tex]2(4-B)=10\quad\Longrightarrow\quad 8-2B=10\quad\Longrightarrow\quad -2B=2\quad\Longrightarrow\quad B=-1[/tex]

Check: with [tex]B=-1[/tex] the function is [tex]f(x)=\frac{2x+1}{3x+4}[/tex], so [tex]f(2)=\frac{5}{10}=\frac{1}{2}[/tex]. Correct.

So [tex]B=-1[/tex].

[Eigenvalue]

[tex]\frac{4-B}{10}[/tex]=[tex]\frac{1}{2}[/tex]
2(4-B)=10
4-B=5
B=-1

[nycmath]

Substitute [tex]x=2[/tex] into the function and set the result equal to [tex]\frac{1}{2}[/tex]:

[tex]f(2)=\frac{2(2)-B}{3(2)+4}=\frac{4-B}{10}=\frac{1}{2}[/tex]

Cross-multiply:

[tex]2(4-B)=10\quad\Longrightarrow\quad 8-2B=10\quad\Longrightarrow\quad -2B=2\quad\Longrightarrow\quad B=-1[/tex]

Check: with [tex]B=-1[/tex] the function is [tex]f(x)=\frac{2x+1}{3x+4}[/tex], so [tex]f(2)=\frac{5}{10}=\frac{1}{2}[/tex]. Correct.

So [tex]B=-1[/tex].

Impressive and direct reply.

[nycmath]

[tex]\frac{4-B}{10}[/tex]=[tex]\frac{1}{2}[/tex]
2(4-B)=10
4-B=5
B=-1

I like your fractional equation setup.