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Determine the input value that produces the same output for two functions.

If [tex]f(x) = -3x + 4[/tex] and [tex]g(x) = 2[/tex], solve for the value of [tex]x[/tex] for which [tex]f(x) = g(x)[/tex] is true.

[tex]x = \square[/tex]



Answer :

GinnyAnswer
To find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex] is true, let's follow these steps in detail:

1. Define the Functions:
- We are given [tex]\( f(x) = -3x + 4 \)[/tex]
- And [tex]\( g(x) = 2 \)[/tex]

2. Set the Functions Equal:
- Since we want to find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex], we set the two expressions equal to each other:
[tex]\[ -3x + 4 = 2 \][/tex]

3. Isolate the Variable [tex]\( x \)[/tex]:
- To solve for [tex]\( x \)[/tex], we first need to isolate [tex]\( x \)[/tex] on one side of the equation. Start by getting all constants on one side:
[tex]\[ -3x + 4 - 4 = 2 - 4 \][/tex]
- Simplify both sides:
[tex]\[ -3x = -2 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
- Now, divide both sides by -3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-2}{-3} \][/tex]

5. Simplify the Expression:
- Simplifying the fraction, we get:
[tex]\[ x = \frac{2}{3} \][/tex]

Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex] is:
[tex]\[ x = 0.6666666666666666 \approx \frac{2}{3} \][/tex]

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