(a) Using the table, give the values fo rthe inverse
1) original table of values:
x 1 2 3 4 5
f(x) 0 1 1 5 3
2) The inverse of the function is obtained by exchanging x and f(x), this is:
( x, f(x) ) → ( f(x), x)
3) So, the table of values of the inverse of the given function is:
x 0 1 1 5 3
f⁻¹ (x) 0 1 2 3 4
(b) Is the inverse a function?
No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.
This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.
The answer:
the full question is if f(x) = 3 [ x - 2 ] , what is f(5.9)?
9
10
11
<span>12
</span>first, [x - 2 ] is called the integer part of x-2,
generally, to compute f(c) where c is a real number, it is sufficient to substitute the value of x by c.
so <span>f(5.9) = 3 [ 5.9 - 2 ] = 3 [ 3.9 ]
as we know that </span>[ 3.9 ]=3
<span>
therefore
</span>3 [ 3.9 ]<span>= 3x3 =9
the answer is 9</span>
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