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katovenus [111]
2 years ago
8

What is the inverse of the function f(x) = 2x - 10?

Mathematics
1 answer:
Oxana [17]2 years ago
3 0

Answer:

h(x) = 1/2x + 5

Step-by-step explanation:

Switch the positions of the x and y (f(x)) and solve for y (f(x)).

f(x) = 2x - 10

x = 2y - 10

x + 10 = 2y

(x + 10)/2 = y

1/2x + 5 = y

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Notation

The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.

Inverses

A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.

A function f -1 is the inverse of f if

<span><span>for every x in the domain of f, f<span> -1</span>[f(x)] = x, and</span><span>for every x in the domain of f<span> -1</span>, f[f<span> -1</span>(x)] = x</span></span>

The domain of f is the range of f -1 and the range of f is the domain of f<span> -1</span>.

Graph of the Inverse Function

The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.

Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.

The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.

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