Hey guys I needed a help Solve 2x -3/x=1
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given
2x - = 1
Multiply through by x
2x² - 3 = x ( subtract x from both sides )
2x² - x - 3 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
The factors are + 2 and - 3
product = 2 × - 3 = - 6 and sum = 2 - 3 = - 1
Use these factors to split the x- term
2x² + 2x - 3x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x + 1) - 3(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
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The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
<h3>How to compare both functions?</h3>The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
Read more about function transformation at:
#SPJ1
