Answer:
x=0.450765 or x=−0.950765
Step-by-step explanation:
14x² + 7x - 6
→ Find the product, sum and factors
Product = -6
Sum = 7
Factors = No factors
→ Since there are no factors utilise the quadratic formula
→ List the values of a, b and c
a = 14
b = 7
c= -6
→ Substitute into the formula
→ Simplify
x=0.450765 or x=−0.950765
Step-by-step explanation:
Swap the sides of the equation :
⤑
We want to remove the 17.56 first.
Since the original equation is 17.56 , we are going to use the opposite operation and subtract 17.56 from both sides :
⤑
Simplify. 17.56 - 17.56 = 0 on the left. 30.16 - 17.36 = 12.6 on the right.
⤑
Then, we need to think about how to remove the coefficient 5. Since the opposite of multiplication is division , I am going to divide both sides by 5.
⤑
Simplify. 5/5 = 1 on the left and 12.6/5 = 2.52 on the right. So, Our answer is x = 2.52.
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Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
which is a cubic polynomial in with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)
Answer:
The quotient rule for exponents states that .
When dividing exponential expressions with the same nonzero base, <u>subtract</u> the exponents.
Step-by-step explanation:
Some rules to solve exponents are:
The quotient rule for exponents states that:
.
When dividing exponential expressions with the same nonzero base, <u>subtract</u> the exponents.