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3 years ago

6

How do i solve this?

1 answer:

n200080 [17]3 years ago

5 0

The polynomial is not factorable, so use the quadratic formula.

y^2 + 8y + 19 = 0

x = (-b +- sqrt(b^2 - 4ac))/(2a)

x = (-8 +- sqrt(8^2 - 4(1)(19))/(2 * 1)

x = (-8 +- sqrt(64 - 76))/2

x = (-8 +- sqrt(-12))/2

If you have not learned imaginary/complex numbers, then the answer is "No solution" since there is no real number solution.

If you have learned imaginary/complex numbers, then we'll continue.

x = (-8 +- 2i sqrt(3))/2

x = -4 +- i sqrt(3)

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Given the function f(x) = 2x, find the value of f−1(32). (1 point) f−1(32) = 0 f−1(32) = 1 f−1(32) = 5 f−1(32) = 16

lara31 [8.8K]

The value of the inverse function at x = 32 will be 16. Then the correct option is D.

<h3>What is a function?</h3>

A statement, principle, or policy that creates the link between two variables is known as a function.

The function is given below.

f(x) = 2x

Then the inverse function of the f(x) will be

2f⁻¹(x) = x

f⁻¹(x) = x / 2

Then the value of the inverse function at x = 32 will be

f⁻¹(32) = 32 / 2

f⁻¹(x) = 16

Then the correct option is D.

More about the function link is given below.

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3 0

2 years ago

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

n200080 [17]

Given:

$f(x)=\dfrac{8}{x}$

$g(x)=\dfrac{8}{x}$

To find:

Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.

Solution:

We know that, two function are inverse of each other if:

$f(g(x))=x$ and $g(f(x))$

We have,

$f(x)=\dfrac{8}{x}$

$g(x)=\dfrac{8}{x}$

Now,

$f(g(x))=f(\dfrac{8}{x})$ $[\because g(x)=\dfrac{8}{x}]$

$f(g(x))=\dfrac{8}{\dfrac{8}{x}}$ $[\because f(x)=\dfrac{8}{x}]$

$f(g(x))=8\times \dfrac{x}{8}$

$f(g(x))=x$

Similarly,

$g(f(x))=f(\dfrac{8}{x})$ $[\because f(x)=\dfrac{8}{x}]$

$g(f(x))=\dfrac{8}{\dfrac{8}{x}}$ $[\because g(x)=\dfrac{8}{x}]$

$g(f(x))=8\times \dfrac{x}{8}$

$g(f(x))=x$

Since, $f(g(x))=x$ and $g(f(x))$ , therefore, f(x) and g(x) are inverse of each other.

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