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Lelu [443]
3 years ago
6

If F(x) = 2 - xand w(x) = x - 2, what is the range of (w•p(x)?

Mathematics
1 answer:
hoa [83]3 years ago
4 0

Answer:

Th Range is [0, -∞)

Step-by-step explanation:

f(x) = 2 - x

w(x) = x - 2

We want to find the range of (f * w)(x).

First, we need to find (f * w)(x), which is the multiplication of the function f(x) and the function w(x). Lets use algebra to find (f * w)(x):

(f*w)(x)=(2-x)(x-2)\\=2x-4-x^2+2x\\=-x^2+4x-4

This is a quadratic function (U shaped), or a parabola. The graph is attached.

The range is the set of y-values for which the function is defined.

We see from the graph that the parabola is upside down and the highest value is y = 0 and lowest goes towards negative infinity. So the range is from 0 to negative infinity. Or,

0 < y < ∞

In interval notation, that would be:

[0, -∞)

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The ratio of two numbers is 4:9. When 5 is subtracted from each of them the new ratio becomes 3:8. Find the numbers.​
natta225 [31]

Answer:

FIRST NUMBER IS 20

AND

SECOND NUMBER IS 45

Step-by-step explanation:

LET THE RATIO BE X

FIRST NUMBER = 4X

SECOND NUMBER = 9X

A/Q,

=}4X - 5 / 9X - 5 = 3 / 8

CRISS CROSS,

=}8 ( 4X - 5 ) = 9X - 5 ( 3 )

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=}5X = 25

=}X = 25 / 5

=}X = 5

THEREFORE,

FIRST NUMBER

=} 4X

=} 5 × 4

=} 20

SECOND NUMBER

=} 9X

=} 5 × 9

=} 45

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