# Answer to Question #5008 in Functional Analysis for Alex

Question #5008

The starting equation for a question is f(x) = x^2 (base parabola function) and i need to change it to g(x) = f[1/4(x + 5)]. Would the point notation be like this: (x, y) --> (4x - 5, y) because the 1/4 inside the brackets is changed to a 4 when doing the point notation?

Expert's answer

If you need to change f(x) to g(x) you have to provide linear substitution x --> 1/4(x + 5):

f(z) = z? = | z:=1/4(x + 5) | = (1/4(x + 5))? = f[1/4(x + 5)] = g(x).

If you need to change g(x) back to f(x) you have to provide linear substitution x --> 4x - 5, it is an inverse problem:

g(z) = f[1/4(z + 5)] = | z:=4x - 5 | = f[1/4(4x - 5 + 5)] = f[1/4(4x)] = f(x).

f(z) = z? = | z:=1/4(x + 5) | = (1/4(x + 5))? = f[1/4(x + 5)] = g(x).

If you need to change g(x) back to f(x) you have to provide linear substitution x --> 4x - 5, it is an inverse problem:

g(z) = f[1/4(z + 5)] = | z:=4x - 5 | = f[1/4(4x - 5 + 5)] = f[1/4(4x)] = f(x).

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