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Zero points

Each number x from the definition range of a function - math problem solver - f for which

f(x) = 0 is called zero of this function.

In investigations of functions with equations of the form y=f (x), function values f (x) are usually first determined for given arguments x, i.e., the values f (x) of the function f at certain points x - homework help at domyhomeworkclub . But also the reverse problem can be of importance, namely

- to determine the points x where the function f has a certain given value f (x),

- to determine the argument x to a given function value f (x),

- to determine the first element for a function given as a pair set to the respective second pair element,

- determine the element of the definition domain that is mapped by f to a given element of the value domain,

or (referring to the graph of f)

determine the abscissa x of a point on the graph - https://domyhomework.club/microeconomics-homework/ - of f that has ordinate y(=f (x)) (interactive computational example 1).

Examples:

Determine the point x where the function f with y=f (x)=3x+5has the value -4.

Solution:

3x+5=- 4 ⇒ 3x=- 9

Thus x=- 3.

Find the argument x to the function value 7 for the function y=f (x)=| x |+3.

Solution:

| x |+3=7 ⇒ | x |=4

In this case there are two arguments (x1=4 and x2=- 4) which have the function value 7. Determine the element x of the definition domain that is mapped to the number 1 by the function

f (x)=x2+4.

Solution: x2+4=1 ⇒ x2=- 3

Since there is no real number whose square is negative, the number 1 cannot be an element of the range of values of f .

Investigate whether the graph of the function f with f (x)=0.5x2- 8has a point with ordinate 10.

Solution:

0.5x2- 8=10 ⇒ 0.5x2=18

So x2 = 36 and therefore x1 = 6 and x2 = -6 .

The points of the graph of f with abscissas x1 = 6 and x2 = -6 have ordinate 10.

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