how to find the zeros of a function

How to find the zeros of functions; tutorial with examples and detailed solutions. The zeros of a function f are found by solving the equation f(x) = 0.

Example one

Find the zero of the linear function f is given by

f(x) = -2 ten + iv

Solution to Case i

To find the zeros of function f, solve the equation
f(10) = -2x + 4 = 0
Hence the goose egg of f is requite past
x = 2

Case two

Find the zeros of the quadratic function f is given by

f(ten) = -2 x ² - 5 10 + vii

Solution to Instance 2

Solve f(10) = 0
f(x) = -2 ten ⁱⁱ - 5 x + 7 = 0
Gene the expression -ii ten ² - vi 10 + 8
(-2x - 7)(x - 1) = 0
and solve for ten
10 = -7 / ii and 10 = 1
The graph of role f is shown below. The zeros of a function are the x coordinates of the x intercepts of the graph of f.

Example 3

Notice the zeros of the sine part f is given by

f(x) = sin(x) - 1 / ii

Solution to Case 3

Solve f(x) = 0
sin (x) - ane / 2 = 0
Rewrite as follows
sin (x) = ane / 2
The above equation is a trigonometric equation and has an infinite number of solutions given by
x = π / 6 + 2 thou π and x = 5 π / 6 + 2 m π where k is whatever integer taking the values 0 , 1, -1, 2, -2 ...
The graph of f is shown below. The number of zeros of function f defined past f(10) = sin(x) - one / ii are is infinite simply because part f is periodic.

Example 4

Find the zeros of the logarithmic role f is given by

f(ten) = ln (x - 3) - 2

Solution to Instance 4

Solve f(x) = 0
ln (x - iii) - 2 = 0
Rewrite as follows
ln (ten - 3) = 2
Rewrite the above equation changing it from logarithmic to exponential class
x - three = east ⁱⁱ
and solve to notice one zero
ten = 3 + e ^two

Example 5

Observe the zeros of the exponential function f is given past

f(x) = e^{x2 - 2} - three

Solution to Example 5

Solve f(x) = 0
e ^{xii - ii} - three = 0
Rewrite the above equation as follows
e ^{102 - two} = iii
Rewrite the to a higher place equation changing it from exponential to logarithmic form
x ⁱⁱ - two = ln (iii)
Solve the above equation to find two zeros of f
x1 = foursquare root [ln (3) + ii]
and
x2 = - square root [ln (3) + 2]

More References and links

Applications, Graphs, Domain and Range of Functions

Source: https://www.analyzemath.com/function/zeros.html

Posted by: newtondictiony.blogspot.com

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