what are real zeroes of this function?
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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 1: Find the zero of the linear function f is given by f(x) = -2 x + 4
Solution to Example 1 To find the zeros of function f, solve the equation f(x) = -2x + 4 = 0 Hence the zero of f is give by x = 2
Example 2: Find the zeros of the quadratic function f is given by f(x) = -2 x 2 - 5 x + 7
Solution to Example 2 Solve f(x) = 0 f(x) = -2 x 2 - 5 x + 7 = 0 Factor the expression -2 x 2 - 6 x + 8 (-2x - 7)(x - 1) = 0 and solve for x x = -7 / 2 and x = 1 The graph of function f is shown below. The zeros of a function are the x coordinates of the x intercepts of the graph of f.
Example 3: Find the zeros of the sine function f is given byf(x) = sin(x) - 1 / 2
Solution to Example 3 Solve f(x) = 0 sin (x) - 1 / 2 = 0 Rewrite as follows sin (x) = 1 / 2 The above equation is a trigonometric equation and has an infinite number of solutions given by x = Pi / 6 + 2 k Pi and x = 5 Pi / 6 + 2 k Pi where k is any integer taking the values 0 , 1, -1, 2, -2 ... The graph of f is shown below. The number of zeros of function f defined by f(x) = sin(x) - 1 / 2 are is infinite simply because function f is periodic.
Example 4: Find the zeros of the logarithmic function f is given by f(x) = ln (x - 3) - 2
Solution to Example 4 Solve f(x) = 0 ln (x - 3) - 2 = 0 Rewrite as follows ln (x - 3) = 2 Rewrite the above equation changing it from logarithmic to exponential form x - 3 = e 2and solve to find one zero x = 3 + e 2
Example 5: Find the zeros of the exponential function f is given by f(x) = ex2 - 2 - 3
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