Answer :
Sure, let's solve each part of the function problem step-by-step!
The given function is [tex]\( f(x) = 5x + 1 \)[/tex].
### a. Find [tex]\( f(29) \)[/tex]
To find [tex]\( f(29) \)[/tex], substitute [tex]\( x = 29 \)[/tex] into the function [tex]\( f(x) = 5x + 1 \)[/tex].
[tex]\[
f(29) = 5(29) + 1 = 145 + 1 = 146
\][/tex]
So, [tex]\( f(29) = 146 \)[/tex].
### b. Find [tex]\( f(-15) \)[/tex]
To find [tex]\( f(-15) \)[/tex], substitute [tex]\( x = -15 \)[/tex] into the function [tex]\( f(x) = 5x + 1 \)[/tex].
[tex]\[
f(-15) = 5(-15) + 1 = -75 + 1 = -74
\][/tex]
So, [tex]\( f(-15) = -74 \)[/tex].
### c. Solve for [tex]\( x \)[/tex] if [tex]\( f(x) = 66 \)[/tex]
We need to solve the equation [tex]\( f(x) = 66 \)[/tex].
[tex]\[
5x + 1 = 66
\][/tex]
Subtract 1 from both sides:
[tex]\[
5x = 65
\][/tex]
Divide by 5:
[tex]\[
x = \frac{65}{5} = 13
\][/tex]
So, [tex]\( x = 13 \)[/tex] when [tex]\( f(x) = 66 \)[/tex].
### d. Solve for [tex]\( x \)[/tex] if [tex]\( f(x) = -7 \)[/tex]
We need to solve the equation [tex]\( f(x) = -7 \)[/tex].
[tex]\[
5x + 1 = -7
\][/tex]
Subtract 1 from both sides:
[tex]\[
5x = -8
\][/tex]
Divide by 5:
[tex]\[
x = \frac{-8}{5} = -1.6
\][/tex]
So, [tex]\( x = -1.6 \)[/tex] when [tex]\( f(x) = -7 \)[/tex].
I hope this solution helps you understand how to work with functions systematically! If you have any more questions, feel free to ask.
The given function is [tex]\( f(x) = 5x + 1 \)[/tex].
### a. Find [tex]\( f(29) \)[/tex]
To find [tex]\( f(29) \)[/tex], substitute [tex]\( x = 29 \)[/tex] into the function [tex]\( f(x) = 5x + 1 \)[/tex].
[tex]\[
f(29) = 5(29) + 1 = 145 + 1 = 146
\][/tex]
So, [tex]\( f(29) = 146 \)[/tex].
### b. Find [tex]\( f(-15) \)[/tex]
To find [tex]\( f(-15) \)[/tex], substitute [tex]\( x = -15 \)[/tex] into the function [tex]\( f(x) = 5x + 1 \)[/tex].
[tex]\[
f(-15) = 5(-15) + 1 = -75 + 1 = -74
\][/tex]
So, [tex]\( f(-15) = -74 \)[/tex].
### c. Solve for [tex]\( x \)[/tex] if [tex]\( f(x) = 66 \)[/tex]
We need to solve the equation [tex]\( f(x) = 66 \)[/tex].
[tex]\[
5x + 1 = 66
\][/tex]
Subtract 1 from both sides:
[tex]\[
5x = 65
\][/tex]
Divide by 5:
[tex]\[
x = \frac{65}{5} = 13
\][/tex]
So, [tex]\( x = 13 \)[/tex] when [tex]\( f(x) = 66 \)[/tex].
### d. Solve for [tex]\( x \)[/tex] if [tex]\( f(x) = -7 \)[/tex]
We need to solve the equation [tex]\( f(x) = -7 \)[/tex].
[tex]\[
5x + 1 = -7
\][/tex]
Subtract 1 from both sides:
[tex]\[
5x = -8
\][/tex]
Divide by 5:
[tex]\[
x = \frac{-8}{5} = -1.6
\][/tex]
So, [tex]\( x = -1.6 \)[/tex] when [tex]\( f(x) = -7 \)[/tex].
I hope this solution helps you understand how to work with functions systematically! If you have any more questions, feel free to ask.
