Let's work through each part of the problem step by step to find the values of [tex]\( x \)[/tex] that satisfy the given equations for the function [tex]\( f(x) = 4x - 2 \)[/tex].
### Part (a)
Given: [tex]\( f(x) = 18 \)[/tex]
1. Start with the equation:
[tex]\[ 4x - 2 = 18 \][/tex]
2. Add 2 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[ 4x = 18 + 2 \][/tex]
[tex]\[ 4x = 20 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{20}{4} \][/tex]
[tex]\[ x = 5.0 \][/tex]
So, [tex]\( x = 5.0 \)[/tex].
### Part (b)
Given: [tex]\( f(x) = 0 \)[/tex]
1. Start with the equation:
[tex]\[ 4x - 2 = 0 \][/tex]
2. Add 2 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[ 4x = 0 + 2 \][/tex]
[tex]\[ 4x = 2 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2}{4} \][/tex]
[tex]\[ x = 0.5 \][/tex]
So, [tex]\( x = 0.5 \)[/tex].
### Part (c)
Given: [tex]\( f(x) = -2 \)[/tex]
1. Start with the equation:
[tex]\[ 4x - 2 = -2 \][/tex]
2. Add 2 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[ 4x = -2 + 2 \][/tex]
[tex]\[ 4x = 0 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{0}{4} \][/tex]
[tex]\[ x = 0.0 \][/tex]
So, [tex]\( x = 0.0 \)[/tex].
### Part (d)
Given: [tex]\( f(x) = 12 \)[/tex]
1. Start with the equation:
[tex]\[ 4x - 2 = 12 \][/tex]
2. Add 2 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[ 4x = 12 + 2 \][/tex]
[tex]\[ 4x = 14 \][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{14}{4} \][/tex]
[tex]\[ x = 3.5 \][/tex]
So, [tex]\( x = 3.5 \)[/tex].
### Summary
The solutions are:
[tex]\[ \text{a) } x = 5.0 \][/tex]
[tex]\[ \text{b) } x = 0.5 \][/tex]
[tex]\[ \text{c) } x = 0.0 \][/tex]
[tex]\[ \text{d) } x = 3.5 \][/tex]
