Question

If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.

Answer 1

Answer

2/3

Explanation

For f(x) = g(x) we should equate the two functions to get the value of x.

f(x) = g(x)

−3x + 4 =  2

-3x + 4 - 4 = 2 - 4

-3x = -2

Dividing by -3 on both sides;

(-3x)/-3 = (-2)/-3

  x = 2/3

Answer 2

²/₃

Further explanation

Given:

$\boxed{ \ f(x) = - 3x + 4 \ }$

$\boxed{ \ g(x) = 2 \ }$

Question:

Solve for the value of x for which f(x) = g(x) is true.

Problem-solving:

We will find out the value of x that makes f(x) = g(x) is true.

$\boxed{ \ f(x) = g(x) \ }$

$\boxed{ \ - 3x + 4 = 2 \ }$

Both sides are subtracted by 4.

$\boxed{ \ - 3x = 2 - 4 \ }$

$\boxed{ \ - 3x = - 2 \ }$

Next, both sides are divided by -3.

$\boxed{ \ x = \frac{- 3}{- 2} \ }$

Thus, the value of x that makes f(x) = g(x) true is $\boxed{\boxed{ \ x = \frac{3}{2} \ }}$

Notes:

• The polynomial functions have any real number as their domain.
• If the function is given by an algebraic expression and the domain is not stated explicitly, then the domain is the set of all real numbers for which the expression is defined as real number $\boxed{ \ \mathbb{R} \ }$.
• To express the domain of a function f(x), we write $\boxed{ \ "x \ \in ..." \ or \ D(f) = ... "\ }$
• The domain of f(x) = -3x + 4 and g(x) = 2 are the same, that is, $\boxed{ \ x \in ( -\infty, \infty ) \ or \ x \in \mathbb{R} \ or \ D(f) = ( -\infty, \infty ) \ or \ D(f) = \mathbb{R} \ }.$ If you choose to write any domain expression from there, then it is still justified.

Equality of function:

Two function f(x) and g(x) are equal if, and only if,

1. $\boxed{ \ f(x) = g(x) \ }$
2. $\boxed{ \ D(f) = D(g) \ }$

Learn more

1. If g(x) is the inverse of f(x), what is the value of f(g(2)) brainly.com/question/1517760
2. The composite function brainly.com/question/1691598
3. The inverse of a function brainly.com/question/3225044

Keywords: ²/₃, f(x) = −3x + 4, g(x) = 2, solve for the value of x, for which f(x) = g(x), true, the domain, any real number, an algebraic expression