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3 years ago

10

Let f be defined as shown on the graph. Which statement is true?

1 answer:

satela [25.4K]3 years ago

4 0

The inverse of f does NOT exist. The reason why is because the function fails the horizontal line test. Recall that the horizontal line test is a test where you try to see if you can pass a single horizontal line through more than one point on the function curve. If you can get the horizontal line to pass through more than one point, then it fails the test. It's very similar to the vertical line test.

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Help! <br> Which expression is equivalent? <br> On edge

Ira Lisetskai [31]

Answer: Choice B

$x^{1/8}y^{8}$

======================================================

Explanation:

The two rules we use are

$(a*b)^c = a^c*b^c$

$(a^b)^c = a^{b*c}$

When applying the first rule to the expression your teacher gave you, we can say that:

$\left(x^{1/4}y^{16}\right)^{1/2} = \left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2}$

Then applying the second rule lets us say

$\left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2} = x^{1/4*1/2}*y^{16*1/2} = x^{1/8}y^{8}$

Therefore,

$\left(x^{1/4}y^{16}\right)^{1/2} = x^{1/8}y^{8}$

-------------

In short, we just multiplied each exponent inside by the outer exponent 1/2.

So that explains why the exponents go from {1/4,16} to {1/8,8} for x and y in that exact order.

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3 years ago