Suppose [tex]$f(x)=4x-2$[/tex]. Determine [tex]$x$[/tex] such that:

a) [tex]$f(x)=18$[/tex]
b) [tex][tex]$f(x)=0$[/tex][/tex]
c) [tex]$f(x)=-2$[/tex]
d) [tex]$f(x)=12$[/tex]



Answer :

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]