What Is Inverse Function In Mathematics?
What is Inverse Function in Mathematics?
In mathematics, an inverse function is a function that “undoes” another function. This means that an inverse function reverses the effect of the original function. For example, if the original function takes an input and produces an output, then the inverse function takes the output and produces the input. So, an inverse function “reverses” the original function.
How to Find the Inverse of a Function
The inverse of a function is found by switching the x- and y-values of the original function. That is, if the original function is y=f(x), then the inverse function is x=f–1(y). This can be written in function notation as f–1(y)=x or f(x)=y–1. You can also find the inverse of a function by solving for y in terms of x, and then switching the x- and y-values.
Examples of Inverse Functions
One example of an inverse function is the reciprocal function. The reciprocal function takes a nonzero number and produces its reciprocal. So, if the original function is y=f(x)=1/x, then the inverse function is x=f–1(y)=1/y. Another example of an inverse function is the square root function. The square root function takes a non-negative number and produces its square root. So, if the original function is y=f(x)=√x, then the inverse function is x=f–1(y)=y2.
Properties of Inverse Functions
Inverse functions have several important properties. First, the inverse of a function is unique. That is, for any given function, there is only one inverse function. Second, the inverse of a function is its own inverse. That is, if f is a function, then f–1 is the inverse of f and f is the inverse of f–1. Third, the inverse of a function reverses the effect of the original function. That is, if f(x) produces y, then f–1(y) produces x.
Applications of Inverse Functions
Inverse functions have many practical applications. For example, they can be used to solve equations. If an equation can be written in the form y=f(x), then the inverse function can be used to solve for x. They can also be used to compute certain integrals, as well as in cryptography and number theory.
Soal dan Jawaban Matematika Fungsi Invers
Soal 1:
Tentukan fungsi invers dari f(x)=x+4?
Jawaban:
Fungsi inversnya adalah f-1(x) = x-4.
Soal 2:
Tentukan fungsi invers dari y=x3?
Jawaban:
Fungsi inversnya adalah y-1= x3.
Soal 3:
Tentukan fungsi invers dari y=log 2 (x)?
Jawaban:
Fungsi inversnya adalah y-1 = 2x.
Conclusion
Inverse functions are an important concept in mathematics. They are used to solve equations, compute integrals, and in many other applications. Inverse functions can be found by switching the x- and y-values of the original function, or by solving for y in terms of x and then switching the x- and y-values. Inverse functions have several important properties, including that they are unique, they are their own inverse, and they reverse the effect of the original function.
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