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An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.

Q: Graph Inverse function of the exponential function?

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No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.

f(x)=2X-2

This question appears to relate to some problem for which we have no information. The graph of an exponential function shows a doubling at regular intervals. But we are not told what the role is of b, so we cannot comment further.

Graph that equation. If the graph pass the horizontal line test, it is an inverse equation (because the graph of an inverse function is just a symmetry graph with respect to the line y= x of a graph of a one-to-one function). If it is given f(x) and g(x) as the inverse of f(x), check if g(f(x)) = x and f(g(x)) = x. If you show that g(f(x)) = x and f(g(x)) = x, then g(x) is the inverse of f(x).

An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.

Related questions

No. The inverse of an exponential function is a logarithmic function.

No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.

Yes.

Logarithmic Function

The inverse function of the exponential is the logarithm.

The logarithm function. If you specifically mean the function ex, the inverse function is the natural logarithm. However, functions with bases other than "e" might also be called exponential functions.

Assuming that b > 0, it is an inverse power function or an inverse exponential function.

The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.

f(x)=2X-2

In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.

The graph of the function y(x) = 1/x is a hyperbola.

Since the logarithmic function is the inverse of the exponential function, then we can say that f(x) = 103x and g(x) = log 3x or f-1(x) = log 3x. As we say that the logarithmic function is the reflection of the graph of the exponential function about the line y = x, we can also say that the exponential function is the reflection of the graph of the logarithmic function about the line y = x. The equations y = log(3x) or y = log10(3x) and 10y = 3x are different ways of expressing the same thing. The first equation is in the logarithmic form and the second equivalent equation is in exponential form. Notice that a logarithm, y, is an exponent. So that the question becomes, "changing from logarithmic to exponential form": y = log(3x) means 10y = 3x, where x = (10y)/3.