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3 years ago

Someone help please

Mathematics

1 answer:

aleksley [76]3 years ago

8 0

9514 1404 393

Answer:

Step-by-step explanation:

The relation between a function f(x) and its inverse g(x) is ...

f(g(x)) = g(f(x)) = x

On can compute these functions of functions, or take an easier route and do the computation with a couple of numbers. It is often easiest to use x=0 or x=1. If we find g(f(x)) ≠ x, then we know the functions are not inverses. If we find g(f(x)) = x for one particular value of x, then we need to try at least one more to verify the relation.

If we call the two given functions f and g, then we have ...

A. f(0) = -2/3, g(-2/3) ≠ 0 . . . . not inverses

B. f(0) = -3/2, g(-3/2) = 0 . . . . possible inverses

f(1) = 4/2 = 2, g(2) = 7/7 = 1 . . . . probable inverses

C. f(0) = -2, g(-2) = 0 . . . . possible inverses

f(1) = 1/2, g(1/2) = -5/3 . . . . not inverses

D. f(0) = 5, g(5) = 27 . . . . not inverses

_____

Additional comment

Our assessment above is sufficiently convincing to let us choose an answer. If we want to verify the functions are inverses, we need to graph them or compute f(g(x)). The graph in the second attachment shows each appears to be the reflection of the other in the line y=x, as required of function inverses.

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Olenka [21]

Answer:

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Step-by-step explanation:

Given:

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.

Now, to find the base and height of the triangle.

The base of triangle = $x\times\frac{1}{2} =\frac{x}{2} \ m.$

The height of triangle = $x\times \frac{3}{4} =\frac{3x}{4}\ m.$

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Now, we put the formula of area to solve:

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$16=\frac{3x^2}{16}$

Multiplying both sides by 16 we get:

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Dividing both sides by 3 we get:

$\frac{256}{3} =x^2$

Using square root on both sides we get:

$\frac{16}{\sqrt{3}}=x$

$x=\frac{16}{\sqrt{3}}$

Now, by substituting the value of $x$ to get the base and height:

$Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.$

So, the base of triangle = $\frac{8}{\sqrt{3}} \ m.$

$Height=x\times\frac{3}{4} \\\\Height=\frac{16}{\sqrt{3}}\times \frac{3}{4} \\\\Height=\frac{12}{\sqrt{3}} \ m.$

Thus, the height of triangle = $\frac{12}{\sqrt{3}} \ m.$

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-----------------------------\\\\

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Answer:

Step-by-step explanation:

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